The obligation to clean one’s house from Chametz:
The Biblical obligation: Biblically, if one nullifies his Chametz and disowns it prior to the 6th hour he is not required to clean his house from Chametz, and the Chametz may rather remain in his home throughout the entire Pesach. If one does not want to nullify it and disown it [or did not do so for whatever reason and the 6th hour has already arrived], then when the time of the Chametz prohibition arrives [the beginning of the 7th hour], he is Biblically obligated to check and search all his possessions for Chametz and completely destroy it from the world.
The Rabbinical obligation: The Sages decreed that nullifying and disowning one’s Chametz before Pesach is ineffective and the Chametz hence remains within one’s ownership, Rabinically. One must thus clean all of his possessions from Chametz before Pesach just like he would Biblically be required to perform if he did not disown it.
Where to check:
One must check and search for Chametz in all areas where there is even suspicion and doubt that perhaps Chametz was brought into it [even] coincidently. This includes even if there is suspicion that perhaps while eating Chametz one entered into that area, and even if one is positive that he never actually ate Chametz there. It goes without saying that all areas which one recalls entering Chametz into even one time during the year, must be checked. Those places which one does not ever remember entering Chametz into them, and it is not common for him to enter the area with food, do not need to be checked. However in homes that there are children, one needs to search for Chametz in all areas that the child can reach, even if one knows that he personally never entered Chametz there.
Does one need to search for even a crumb of Chametz?
One must search for even a crumb of Chametz and destroy it as the Sages decreed against owning even less than a Kezayis of Chametz, lest one come to own a Kezayis. This applies even if one has already nullified his chametz, or plans to nullify it before Pesach. If however the Chametz is dirty and one has already nullified his Chametz, or plans to do so before the 6th hour, then if the Chametz is less than the size of a Kezayis, one is not required to search for this Chametz or destroy it.
Crumbs of Chametz found in areas that people walk: One only has to search for slightly large crumbs of Chametz which are on the floor, although thin crumbs of Chametz, even if one sees them lying on the ground, one does not need to gather them and burn them if they are in an area where people step on, being that they end up getting destroyed on their own through stepping on them. Although if one sees them on the floor after the 6th hour, then one must gather them and destroy them.
Chametz which is found in areas that are not reachable by hand:
Chametz that is in cracks and crevices of tiles and furniture:
If one cannot remove the Chametz with his hands due to it being stuck under cracks and crevices and the like then it suffices for him to nullify this Chametz before the 6th hour [through saying the Bitul of Kol Chamira], and if he plans to do so he is not required to destroy this Chametz before Pesach. One is not required to undo the floor [or to undo furniture] to remove the Chametz even if he is capable of doing so, and rather the nullification suffices. This applies even if one is able to see the Chametz. This applies even if there is a Kezayis of Chametz. Thus the Chametz that is in between the deep crevices of one’s floor between the tiles [or in the cracks of one’s table or other furniture], does not need to be removed or destroyed but is to be merely nullified. [If one did not nullify his Chametz and did not sell it before Pesach then he must destroy this Chametz on Pesach upon remembering even if it entails taking apart the furniture and the like.]
All the above is from the letter of the law, however practically the Jewish people are holy and hence the custom is to destroy all Chametz that is in one’s possession, even the Chametz found in unreachable areas. One is thus to pour bleach or other spoiling agent over Chametz that he is unable to reach with his hands.
A Chassidic perspective-The Holiness of the Job:
We can learn from the following story, the great holiness involved in cleaning for Pesach: It occurred one year on Rosh Hashanah, after Reb Levi Yitzchak of Berditchiv blew the Shofar, that he exclaimed “Sweet Father, if the angles which were created from the Shofar blowing of Levi Yitzchak the son of Sara are weak, let the holy and healthy angels which were created from the hard work and toil of your people before Pesach, in which they scrubbed, smoothened and Kashered in honor of Pesach and for Hiddur Mitzvah; let those angels come and appease you.”
Background from 431/2 [Translation]:
If rather than destroying the Chametz one wants to just nullify it and disown it, its meaningless [regarding fulfilling the Torah command] once the Biblical time of the eating and benefit prohibition of Chametz has arrived, which is from midday of the 14th and onwards, as since one is prohibited from benefiting from it, he no longer retains any rights to the Chametz, and [is thus] not his at all [anymore], therefore he can no longer nullify and disown it, [as it is no longer legally owned by him.] However before the time of the benefit prohibition [arriving] one may nullify and disown the Chametz, and may [after doing so] Biblically leave the Chametz with him in his house throughout all the days of Pesach, as one only Biblically transgresses baal yiraeh and Baal yimatzeh on Chametz that he owns which he has not disowned, as the verse states “You shall not see to you”, that your own Chametz you may not see, however you may see the Chametz of others and that is disowned.
Rabbinically may only nullify until 6th hour of day[433/30]: [The above ability to disown the chametz until midday is only from a Biblical perspective, however Rabinically] once the beginning of the 6th hour of the day has arrived one is no longer able to nullify the Chametz being that the sages decreed that from the [beginning of the] 6th hour and onwards one cannot get any benefit from the Chametz, thus starting from the [beginning] of the 6th hour one no longer has any portion or rights to the Chametz, and it is thus not considered his for him to be able to nullify it and disown it.
 As one only Biblically transgresses baal yiraeh and Baal yimatzeh on Chametz that he owns which he has not disowned, as the verse states “You shall not see to you”, that your own Chametz you may not see, however you may see the Chametz of others and that is disowned. [ibid]
Background from 431/3 [Translation]:
[The above ability to do bittul and disown the Chametz before the 6th hour and then be able to leave the Chametz in his home is only from a Biblical perspective, however] the sages decreed that doing bittul and disowning the Chametz is meaningless to [avoiding the prohibition of owning] the Chametz even when done before the time arrives for the benefit prohibition [the 6th hour]. Rather they decreed that one must search after the Chametz in the holes and hidden areas, if it is common to use these areas throughout the year, and to check and remove any Chametz found from/within his entire property, and [destroy it or places it in a public area, as will be explained]
 The reason for this decree [431/4]:
There are two reasons why the sages made the above decree [that the Chametz may not remain in one’s home even if nullified and disowned].
First Reason [Rashi]: The reason why the Sages made the nullification ineffective is because nullifying and disowning the Chametz is dependent on ones thought, [meaning] that he disown the Chametz with a full heart, and remove it completely from his heart. Now, since not all peoples thoughts/Daas are alike, and it is [thus] possible that one may be lenient in this and will not disown it with a full heart, and will not remove it from his heart completely, therefore the sages decreed that nullification and disowning is meaningless unless one actually removes all his Chametz from his property.
The second reason [Tosafus][for why they decreed that the Chametz be removed from ones property] is because people are accustomed throughout the year to eat Chametz, and due to this habit it is very possible for him to come to forget about the prohibition of eating Chametz, and he will thus come to eat Chametz if it is lying in his property on Pesach. Therefore the sages required that one search and check for Chametz and remove it.
[Although these two reasons are mentioned] the main reason of the sages for one to search for Chametz, despite having nullified it, is because of a decree that perhaps one will come to eat it on Pesach. [433/19]
Background from 433/12-13:
A. The areas which must be searched Biblically:
Areas which one is Biblically obligated to check-Contains Kezayis of Chametz: Biblically, [i.e. when doing the bedikah because he has not nullified his Chametz] he is only obligated to search for Chametz in areas which one commonly uses Chametz in frequently throughout the year, such as ones living room/kitchen and the bedrooms which one eats Chametz in throughout the year, and it is therefore impossible that a kezayis of Chametz has not crumbled and fallen into those areas, of which one Biblically transgresses baal yiraeh and baal yimatzeh throughout all the days of Pesach even if they are not visible to him. However the other rooms which one does not commonly use Chametz in them frequently throughout the year, and it is thus probable that a kezayis of Chametz has not remained in them, do not have to Biblically be checked even though one did not nullify his Chametz. [433/12]
The reason [433/25]: for this is because Biblically we do not suspect for such a doubtful situation of Chametz being present, [as perhaps Chametz was never entered into there, and perhaps even if it was it was all removed, and even if some Chametz did remain, perhaps it occurred many days before Pesach and it has spoiled by now and is no longer edible for a dog]. Thus being that Biblically we follow the rule that we do not assume for bad, and rather assume that it is clean of Chametz, therefore Biblically these areas do not have to be checked.
B. The areas which must be searched Rabinically:
Any area with suspicion of even a crumb of Chametz: Rabinically, even if one has nullified all his Chametz, one must check and search for Chametz in all areas where there is [even] suspicion and doubt that perhaps Chametz was brought into it by chance. [433/13]
The reason for this [433/25]: is because due to the stringency of the Chametz prohibition, the sages suspected for even a case that there is doubt of Chametz, and they therefore enacted the mitzvah of bedikah. Thus it makes no difference if there is only one doubt involved or many doubts involved, as either way they suspected for all doubts of Chametz.
 This applies even if there are many doubts involved to be lenient, such as perhaps Chametz was never entered into there, and perhaps even if it was it was all removed, and even if some Chametz did remain, perhaps it occurred many days before Pesach and it has spoiled by now and is no longer edible for a dog. The reason for this is because due to the stringency of the Chametz prohibition, the sages suspected for even a case that there is doubt of Chametz, and they therefore enacted the mitzvah of bedikah. Thus it makes no difference if there is only one doubt involved or many doubts involved, as either way they suspected for all doubts of Chametz. [433/25]
 433/13; 442/28; 444/9; 446/3
In the end of 433/13 Admur says that one needs to check for even “Shum Pirur Chametz” and in 442/28 that Rabinically one may not own even less than a Kezayis. In 444/9 Admur rules that one needs to destroy the small leftover crumbs when Erev Pesach falls on Shabbos, and in 446/3 that on Pesach one must destroy even less than a Kezayis of Chametz which one has done bittul to.
 This applies in a case that one did not nullify his Chametz before Pesach or does not plan to do so. In such a case one transgresses a Rabbinical prohibition of Baal Yiraeh over such Chametz, even though it is less than a Kezayis.
 One must search for even less than a Kezayis crumb of Chametz which is anyways nullified because one may come to inadvertently eat it if one were allowed to own it, and not because of a Rabbinical Baal Yiraeh. [446 Kuntrus Achron 1] Therefore one does not say a blessing of bedikas Chametz if one only has suspicion that less than a Kezayis of Chametz has remained to be checked for. [432/5]
 442/28; See Halachic analysis for explanation.
For this reason some rule one does not need to destroy Chametz crumbs that is found in books, or that are on the floor where people step on.
 Vetzaruch Iyun why are the crumbs on the floor not considered dirty and thus inedible and thus do not need to be destroyed if one did bitul, as explained in 442
Background from Admur:
Chametz found in the cracks of a wooden plank floor [433/19]: If ones has a floor which has small deep cracks in between the tiles, such as by a wooden board floor which has small deep cracks in between the planks of wood, then if one is unable to enter his hand into the hole to check for Chametz, he does not need to remove the tiles/wood in order to allow him to check under them. Even if one sees that Chametz has fallen into one of the small holes, and if one does not remove it, then it will be there throughout all the days of Pesach, nevertheless we do not trouble him to remove it from there, rather he nullifies it and that suffices.
Chametz is inside hole of wall[433/20]: Similarly by a hole in ones wall or floor which is wide enough for one to fit his hand in, but is very deep, that one is not able to enter his hand to search the entire hole for Chametz, then one checks the hole to as deep that his hand reaches, and the remaining area suffices with ones nullification, even if there is certainly Chametz there.
 The reason for this is because the main enactment of the sages for one to search for Chametz, despite having nullified it, is due to a decree that one may come to eat it on Pesach. Now, in the above case being that this Chametz is in an area which one cannot place his hand in, certainly he will not come to eat it on Pesach. [433/19] Now, although by a Mapoles of less than three Tefachim the Sages nevertheless required one to destroy the Chametz, this is only because the Chametz may come to be revealed by a dog or because the mound may become revealed. However here by Chametz stuck between cracks, or in a deep pit there is no possibility for a dog to reveal the Chametz, or for it to happen on its own, as is common by a mound. [Kuntrus Achron 4]