Is Shemitah today Biblical or Rabbinical?
Some Poskim rule it is of Biblical obligation. Other Poskim rule that the observance of Shemitah in today’s times is of only Rabbinical obligation. Other Poskim rule that it is not at all obligatory today, even on a Rabbinical level, and is only observed due to Midas Chassidus. Majority of Poskim negate this latter opinion. Practically the accepted Halachic ruling is that Shemitah today is of Rabbinical obligation.
Shemitas Kesafim: [Biblically the command to annul loans during Shemitah only applies during times that the Yovel cycle is in practice, which is when all the tribes are living in Eretz Yisrael.] In today’s times [however] the laws of Shemitas Kesafim [abolishing debts] during the year of Shemitah is [only] a Rabbinical enactment. This applies in both Eretz Yisrael, and in the Diaspora.
 See Mitzvas Hashemitah chapter 2
Many commands in the Torah are contingent on different factors for them to be in effect. Some are dependent on one’s living in Eretz Yisrael. Others are dependent on the establishment of the Temple. Others are dependent on the inhabitation of all the Jewish people in Eretz Yisrael. Others are dependent on the holiness of the land of Eretz Yisrael. Others are dependent on a number of these factors.
Not dependent on Temple: According to all opinions the command of Shemitah is independent from the establishment of the Temple. Hence even when the Temple is not in existence it is still possible for Shemitah to be a Biblical obligation. [Rambam 4/25] In fact, the first cycles of Biblical Shemitah that was observed by the Jewish people was before the Temple was even established and hence it cannot possibly be dependent on it. [Toras Kohanim Behar 1/3]
Dependent on Kedushas Eretz Yisrael: The Mitzvah of Shemitah is only Biblically applicable when Eretz Yisrael contains its Holiness. Eretz Yisrael was first sanctified when the Jewish people conquered Eretz Yisrael in the times of Yehoshua. [See Rambam Teruma 1/2] The exile after the destruction of the first Temple revoked this sanctity and hence the land reverted to its unsanctified state in which the Mitzvah of Shemitah was no longer Biblical. [Rambam ibid; Rambam Beis Habechira 6/16] When the exiles returned from Bavel to Eretz Yisrael they re-sanctified the land of Israel with Ezra leading the way. [Rambam Terumos 1/5] Thus the Mitzvah of Shemitah returned to a Biblical state. Certain sections of Eretz Yisrael that were originally sanctified, however were not re-sanctified by the return of Ezra with the Babylonian exile and hence remained desolate of its previous Holiness, and Shemitah did not Biblically apply in those regions. [See Yevamos 16a; Rambam 4/26] After the destruction of the 2nd Temple and the second exile it became disputed as to whether Eretz Yisrael once again lost its holiness, as occurred after the first exile, or if the sanctification performed by Ezra was permanent and hence remains intact even now. [See Megillah 10; Chagiga 3b; Yevamos16a; 82b; Shavuos 16a; Makos 19a; Chulin 7a; Erechin 32b] Some Poskim rule that Eretz Yisrael once again lost its holiness and hence all Mitzvos of the land, including Shemitah lost their Biblical status. [Rashi in Gittin 36a; Sanhedrin 26a; Tosafus Yevamos 82b; Tur Yoreh Deah 331] Other Poskim however rule that it retains its Holiness and hence the land dependent Mitzvos enjoy a Biblical status. [Rambam Beis Habechira 6/16; See Michaber 331/1]
Complete Jewish inhabitation of Eretz Yisrael: It is disputed amongst Poskim as to whether the Biblical observance of Shemitah is dependent on the inhabitation of the entire Jewish people in Eretz Yisrael. Some Poskim rule it is dependent on it and hence even if one learns that the Holiness of Eretz Yisrael is still active, nevertheless Shemitah is not Biblically obligatory. [Beis Yosef 331; Kesef Mishneh 4/24; Rambam Terumos 1/26 regarding Teruma and so understands in his opinion Rabbeinu Chaim Halevi Shemita 12/16; Michaber 331/1 regarding Teruma ] Others however rule that the Biblical observance of Shemitah is independent of the inhabitance of all the Jewish people in Eretz Yisrael [Raavad Terumos 1/26], and hence it would be a Biblical obligation according to those who learn the Holiness of Eretz Yisrael is now eternal.
Yovel: It is disputed amongst the Tannaim in the Mishneh as well as the Poskim as to whether the Biblical observance of Shemitah is dependent on the Biblical observance of Yovel. Some Poskim rule it is dependent on it and hence even if one learns that the Holiness of Eretz Yisrael is still active, nevertheless Shemitah is not Biblically obligatory. [Rebbe Gittin 36a; Rashi ibid; Yerushalmi 6/2; Rambam 10/9] Others rule it is independent of Yovel. [Chachamim Gittin 36a; Ramban ibid; Kesef Mishneh 9/2 in opinion of Rambam; See Beis Halevi 3/1 that so hold majority of Rishonim]
 Chachamim Gittin 36a; Ramban ibid; Kesef Mishneh 9/2 in opinion of Rambam; See Beis Halevi 3/1 that so hold majority of Rishonim
 The reason: As Shemitah is not dependent on Yovel or all Jewish inhabitation and Eretz Yisrael has not lost its holiness hence fulfilling all the criteria necessary to deem Shemitah Biblical.
 Rebbe Gittin 36a; Yerushalmi 6/2; Rambam 10/9; Rashi in Gittin 36a; Sanhedrin 26a; Tosafus Yevamos 82b; Ritva Gittin ibid; Rashba 775; Smag 148 and negative 271; Smak 258; Hayireim 164; Hachinuch 84 and 475; Tur Yoreh Deah 331; Beis Yosef 331; Kesef Mishneh 4/24 Peas Hashulchan 23/23; Sheilas David; Shevas Haaretz; Chazon Ish Shevis 3/7
 The reason: As Eretz Yisrael lost its holiness after the destruction of the second Temple. Alternatively because not all Jews live in Eretz Yisrael, Alternatively because Shemitah is dependent on Yovel and today Yovel is not accustomed.
 Sefer Haterumos 45 in name of Razah; Meiri Gittin 36a; Raavad on Rif Gittin ibid
 The reason: As Shemitah is dependent on the Yovel and hence since today the Yovel is not in practice even Rabbinically therefore Shemitah is also not in practice even Rabbinically.
 Sefer Haterumos ibid; Beis Yosef Choshen Mishpat 67; Chazon Ish 23/4; Some record that the Ravaad retracted his ruling.
 Ritva Gittin ibid; Rashba 775; Smag 148 and negative 271; Smak 258; Hayireim 164; Hachinuch 84 and 475; Tur Yoreh Deah 331; Peas Hashulchan 23/23; Sheilas David; Shevas Haaretz; Chazon Ish Shevis 3/7
 Admur Hilchos Halva 34
 Michaber 67/1; Rambam Shemitah 2/9
Other Opinions: See Ramban brought in Urim Vetumim 67/1 that holds Shemitas Kesafim is a Biblical obligation even today, and even in the Diaspora.
 Rambam Shemitah 10/8
 Admur 34; Gittin ibid; Rambam 9/3; Michaber ibid
 Admur ibid; Michaber ibid