The custom of all Jewry is that the reader unrolls the Megillah and folds it like a letter.
When is the Megillah to be folded like a letter? The Megillah is to be unrolled and folded like a letter prior to the start of the reading. This is to be done prior to the blessings that are said before the reading.
When is the Megillah to be rolled back up? The Megillah is to remain [completely] folded until the end of the reading. After completing the reading, one is to roll up the entire Megillah and then say the after blessing of רב את ריבנו [while the Megillah is still lying in front of him]. [Some Poskim however rule that one may choose to leave the Megillah folded while reciting the blessings and then roll it up after the blessing is completed. Practically the Chabad custom is to say the blessing before rolling up the Megillah.]
Are also the listeners to fold their Megillahs? The above law of folding the Megillah only applies to the Megillah of the Baal Korei and not to the individual Megillah of a listener. Nevertheless many listeners have the custom to also fold the Megillah. [Practically the Chabad custom is that also those listening to the reading of the Megillah fold their scroll like a letter, into three parts.]
Making sure the Megillah does not touch the floor: One must beware that the unrolled Megillah does not touch the floor. Furthermore one is to prevent the unrolled Megillah from hanging over the side of the table over the floor.
The Megillah is to be unrolled and folded into three parts like a letter prior to beginning the blessings over the Megillah. It is to remain completely folded until the reading is complete. The Chabad custom is to begin rolling it back up only after the after blessing has concluded.
 Michaber ibid; Admur in Siddur; based on Rav Haiy Gaon brought in Tur and so was custom in Spain, France and Germany, and so ruled Rif, Rosh and Rambam.
Other Opinions: Rav Neturaiy Gaon [brought in Tur] writes that in two Yeshivos in Baval they would roll the Megillah like a Sefer Torah.
 Bach; Taz 690/10; Admur in Siddur; Drashos Maharil [Hilchos Purim]; Teshuvas Maharil 56; Levush; Shiyurei Knesses Hagedola 690/5; Peri Chadash; Elya Raba 690/12; Chayeh Adam 151/23; P”M 690 M”Z 10; M”B 690/56; Kaf Hachaim 690/102.
Other Opinions: The above is based on the Tur; Bach and other Poskim ibid that rule according to Rav Haiy Gaon one is to completely unroll it before the start of the reading. However many other Poskim rule that according to Rav Haiy Gaon one is to begin with a rolled Megillah and unroll it as he goes along, leaving the read area unrolled. This is also clearly implied in the words of the Michaber ibid which writes “The reader is to read and unfold…”. [Taz 690/10 in understanding of Michaber ibid] Practically the Bach; Taz ibid and all Poskim ibid conclude the custom is to completely unfold it before the reading.
 P”M 690 M”Z 10; M”B 690/56; Kaf Hachaim 690/103; Admur in Siddur
The reason: The reason for this is because unrolling it between the blessing and the start of the reading would constitute an interval. [ibid]
 Michaber ibid
 Otzer Minhagei Chabad Purim 87; See there that the Rebbe did not roll up the Megillah as the reading went along. This is unlike Teshurah Chasunah 1995 that understood from a certain picture that the Rebbe rolled up the Megillah as he went along, and so wrote Hiskashrus 36 p. 14 that it was a onetime occurrence. However in truth after looking at a clearer picture of that incident it comes out that the Megillah was not rolled at all and the end of the Megillah looks a bit rolled and hence they thought the Rebbe rolled it as the reading went along. [Otzer ibid]
 Drashos Maharil Purim; Mateh Moshe 1005; Levush; M”A 690/19; Elya Raba 690/10; Chayeh Adam 154/25; M”B 690/57; Kaf Hachaim 690/105
 The reason it is rolled before the after blessing: The reason for this is because it is a belittlement towards the Megillah to leave it unrolled while the blessing is being said. [Drashos Maharil ibid; Elya Raba ibid; Chayeh Adam ibid; M”B ibid] Alternatively the reason is because the after blessing is a mere custom and is not required due to the letter of the law. Hence in order to emphasize the difference in Halachic weight of the two blessings we roll the Megillah before the after blessing. Alternatively the reason is so people do not think that the blessings are written in the Megillah. This is similar to the law regarding closing the Torah scroll while the blessings are recited. [Rebbe in edited Sicha of Purim 1956 printed in Shevach Hamoadim 127; Shulchan Menachem 3/317]
If one already began saying the blessing: If one did not yet say Hashem’s name and simply said Baruch Ata, then he is to stop and roll up the Megillah and then restart the blessing. [Drashos Maharil ibid; Mateh Moshe ibid; Elya Raba ibid; Chayeh Adam ibid; M”B ibid]
 M”A 690/20 based on Shiyurei Kneses Hagedola 692; Seder Hayom; Beir Heiytiv 690/13; Ashel Avraham Butchach 692 [there he writes that the listeners are specifically to roll up their Megillah after the blessing and the above law was only said regarding the reader.]
The reason behind their ruling: It is not a belittlement towards the Megillah to leave it open during the blessings as the blessings are in relation to the reading. Likewise there is no need to emphasize the difference in Halacha between the before and after blessing just like this is not done by the before and after blessings of Hallel. Likewise the same way we allow the Megillah to be open during the before blessings, without worry that people may think the blessings are written in the Megillah, so too by the after blessings. [Rebbe in edited Sicha of Purim 1956 printed in Shevach Hamoadim 127; Shulchan Menachem 3/317; See Shaareiy Halacha Uminhag 5/94]
Other Opinions: Many Poskim argue on this ruling of the M”A and Seder Hayom. [Drashos Mahril ibid; Mateh Mohe ibid; Elya Raba ibid; Gr”a ibid; Kaf Hachaim 690/105]
 Rebbe in edited Sicha of Purim 1956 [printed in Shevach Hamoadim 127; Shulchan Menachem 3/317; See Shaareiy Halacha Uminhag 5/94; Hiskashrus 1025 footnote 43] See Otzer Minhagei Chabad 106 that in conclusion the Rebbe directed the congregation to roll the Megillah after the blessing in order to draw down extra Divine light of the Megillah into the blessings.
Opinion of Admur in the Siddur: Admur in the Siddur does not state when it is to be rolled up, despite the fact he mentions unrolling it before the reading. This implies that Admur rules like the M”A that one can roll it up after the blessing. [Rebbe ibid]
The Rebbe’s personal custom: Some years the Rebbe began rolling up the Megillah immediately after the reading, as soon as the after blessing began. He continued rolling it during the blessing and then stopped to say Shoshanas Yaakov and then finished the rolling. [Otzer Minhagei Chabad 107] This is not a directive to the public. [Hiskashrus 1025]
 Michaber ibid
 Sefer Haminhagim [English] p. 170; Reshimos 177/4 in name of Rebbe Rayatz
Other Opinions: Many Poskim rule it is to be folded one page [Yeria] over the other. [M”B 690/56; Chayeh Adam 154; Ben Ish Chaiy Tetzaveh 4; Aruch Hashulchan 690/22
 Bach; Elya Raba 690/12; Chayeh Adam 154/23; M”B 690/55
 P”M 690 A”A 18; Shaar Hatziyon 690/50; Kaf Hachaim 690/104 based on Drashas Mahril that if one is reading from his Megillah to fulfill his obligation then he is to fold it [even if he is reading along with the reader] and certainly if he is reading without a Minyan. However see Likkutei Maharich that there is no need to fold it when one is reading it alone.
 Sefer Haminhagim [English] p. 170; The Rebbe there [footnote 683] mentions in footnote that perhaps the reason is because one who has Kosher Megillah is to read along with the reader in order so he does not miss one word, as rules P”M 689. [This is similar to the inference of the Kaf Hachaim ibid from the Mahril.]
 Peri Chadash; Elya Raba 690/12; P”M 690 M”Z 10; M”B 690/56; Kaf Hachaim 690/103
 P”M 690 M”Z 10; M”B 690/56; Kaf Hachaim 690/103
The reason: As this is a belittlement for the Megillah. [ibid]