The gemara discusses the concept of the kedusha of the land and whether the original kedusha remains even after the destruction of the beis hamikdash. Simply learning our gemara according to rashi would lead to the conclusion that the kedusha of E.Y. and Yerushalayim/mikdash are completely tied to one another, and that we conclude קדושה ראשונה קדשה לשעתה ולא קדשה לעתיד לבא. Therefore, any halachos that are tied to E.Y. such as Teruma and Ma'aser and halachos that are tied to Yerushalyim such as the issur to bring korbanos on bamos and the ability to eat ma'aser sheini in yerushalayim, no longer apply. The continuation of tithing teruma and ma'aser would only be d'rabonon. However, Tosafos has difficulty with this girsa and argues on both assumtions. Tosafos holds that the discussions in the gemara regarding the kedusha of E.Y. are completely independent of those regarding the kedusha of Yerushalayim. In both places the phrase קדושה ראשונה קדשה לשעת ולא קדשה לעתיד לבא can be used, but means totally different things. Therefore, Tosafos holds that although we have other sources that indicate that the kedusha of E.Y. no longer exists m'doraysa regarding teruma and ma'aser, the kedusha of Yerushalaim was never lost and remains strong. The conclusion of our gemara is that the kedusha of Yerushalayim is still in tact, yet one cannot eat b'chor and ma'aser in Yerushalayim due to a technicality - The ability to eat a b'chor is tied to the ability to sprinkle the blood. So long as there is no altar on which to sprinkle the blood, the b'chor cannot be eaten, and the ma'aser sheini can also not be eaten.
The approach of Tosafos is necessary to explain the position of the Rambam. The Rambam (Hil. Beis HaBechira 6:14-16) explains the process of sanctifying the beis hamikdash and courtyard. Rambam writes that when Ezra returned he only brought 2 korban todos as a symbolic kiddush, but in actuality the beis hamikdash and Yerushalayim retained their original kedusha from the time of Shlomo HaMelech. Therefore the Rambam rules that korbanos can be brought in the makom of the mizbei'ach even in the absence of a beis hamikdash, and kodshim can be eaten (kodshei kodshim in the courtyard and kadshim kalim in Yerushalayim). Then the Rambam writes:
ולמה אני אומר במקדש וירושלים שקדושה ראשונה קדושתן לעתיד לבא ובקדושת שאר ארץ ישראל לענין שביעית ומעשרות וכיוצ"ב לא קדשה לעתיד לבוא? לפי שקדושת המקדש וירושלים מפני השכינה ושכינה אינה בטלה, והרי הוא אומר "והשמותי את מקדשכם" ואמרו חכמים אע"פ ששוממין בקדושתן הן עומדים. אבל חיוב הארץ בשביעית ובמעשרות אינו אלא מפני שהוא כבוש רבים וכיון שנלקחה הארץ מידיהם בטל הכבוש ונפטרה מן התורה מן המעשרות ומן השביעית שהרי אינה ארץ ישראל
The Rambam holds that the kedusha of E.Y. is the "kibbush" - Jewish control, therefore when it reverts back to the goyim, the kedusha is lost. But the kedusha of the mikdash and Yerushalayim is attributed to the shechina which never leaves (the rambam concludes by making a distinction between kibbush (capture) and chazaka (control), and writes that Ezra took control of E.Y. which restored its kedusha even after it was taken back by the goyim - this approach if very difficult - see kesef mishna).
The Ra'avad adamantly disagrees with the Rambam and assumes that since ma'aser sheini cannot be eaten, the kedusha of Yerushalayim and the mikdash must be gone, just as it is gone from the rest of E.Y. Furthermore, even the opinion who holds that E.Y. retains it's kedusha would admit that Yerushalayim and the mikdash lose their kedusha upon the destruction of the mikdash.
There is a very practical difference between the Rambam and Ra'avad. Is one allowed to walk into the place of the mikdash nowadays, while they still have tu'mas meis. According to the Ra'vad there wouldn't be any issur kareis, but according to the Rambam it would be an issur kareis (of course, the areas which only have status of machane leviyim, one can technically go even as a tamei meis, so long as they are don't have tu'mas keri).
The kesef mishna points out that the Ra'avad's question on the Rambam from mishnayos that say that ma'aser sheini has to rot and cannot be eaten in Yerushalayim, is a difficulty with the Rambam. However, the Mishneh L'melech explains that the Rambam in Ma'aser Sheini (chapter 2) indicates that he holds like Tosafos in our sugya, that for technical reasons of comparing ma'aser sheini to be'chor it cannot be eaten. But the kedusha of Yerushalayim is still intact. The Magen Avrohom (561:2) writes explicitly that the Rambam will hold like Tosafos in our sugya. Therefore, he concludes - דברי הרמב"ם שרירין וקימים והנכנס עתה למקום המקדש חייב כרת שכולנו טמאי מתים
It is for this reason that those who go up on the har habayis after going to the mikva and waiting for sunset to remove tu'mas keri, have to be confident that they are not overstepping the machaneh l'viya, because by walking into the machane shechina even nowadays would be an issur karies (since our Tosafos answers up the opinon of the Rambam, thus compels the magen avraham to pasken like the Rambam, not the Ra'avad).
To conclude, it is important to see the Chasam Sofer (Y.D. 233: second paragraph, 234 d.h. v'hinei) where he puts the Rambam and Ra'avad in perspective. The Chasam Sofer considers the discussion of whether E.Y. and Yerushalayim retain their kedusha regarding mitzvos, completely independent of the mitzvah to live in E.Y. and Yerushalayim. The mitzvah of living there is connected to their inherent kedusha and being a place of tefila even before the existence of the beis hamikdash. The chasam sofer suggests that according to those who hold that the kedusha for mitzvos is lost, would not even have the excuse that R. Chaim Kohen (Tosafos in Kesubos) offers to justify not living in E.Y. because it difficult to keep the mitzvos. Since the mitzvos aren't considered d'oraysa, the excuse is not applicable so the requirement to live in E.Y. and Yerushalayim is even stronger. He enforces this point by citing the famous Rambam in sefer HaMitzvos 153 who says that the ability of klal yisroel to establish the calendar and yomim tovim (even nowadays) is dependent on Jews living in E.Y. -
נראה מדבריו (רמב"ם) כי אילו ח"ו לא ישאר שום ישראל בארץ ישראל אפילו יהיה יושבים ישראל בחו"ל מקרי כליון אומה ח"ו אחר שאין לנו סמוכים ואי אפשר לקבוע חדשים ולעבר
The chasam sofer considers the Rambam's statement that if Jews wouldn't be in E.Y. it would qualify as a destruction of the nation, to be because of our inability to establish the calendar. However, it is possible that the Rambam means something even deeper. Perhaps the status of "klal yisroel" is dependent on the existence of Eretz Yisroel, therefore if E.Y. would be empty without any Jews living there, it would impact the status of "klal yisroel" and they would lose that title.