The basic halacha is that Kriyat Shema with its brachot must be recited within the window Chazal set for the mitzvah, which runs from when one can distinguish tekhelet from white until the end of three halachic hours, a quarter of the day, as stated in the Mishnah (Berakhot 9b:9-10) and codified by Shulchan Arukh, Orach Chayim 58:1, the Tur, Orach Chayim 58, and Mishneh Torah, Reading the Shema 1:13.
If one misses that window, the Rambam rules that one has not fulfilled the mitzvah in its proper time and the recitation becomes like reading Torah, though one still recites the brachot before and after it the entire day even if delayed past three hours (Mishneh Torah, Reading the Shema 1:13), a leniency echoed by Kitzur Shulchan Arukh Yalkut Yosef, Orach Chaim 58:6 and Kaf HaChayim on Shulchan Arukh, Orach Chayim 58:3-8, which extend the time for the brachot themselves until the end of the fourth hour even though the primary mitzvah time for Shema itself has passed.
Mishnah Berurah 58:2 explains the reasoning behind the cutoff: because the Torah phrase "uvekumecha" ties the mitzvah to the time people actually rise, and because the parshah of tzitzit within Shema speaks of "וראיתם אותו," the Sages fixed the starting point at the ability to recognize a slight acquaintance at four amos, which correspondingly bounds the end of the proper window.
Shulchan Arukh HaRav, Orach Chayim 58:3 and Kitzur Shulchan Arukh 17:1 likewise affirm that the time extends only until the end of the third proportional hour, a quarter of the halachically defined day, and caution that in winter when the day is short one must hurry to recite Shema within that narrower window.
Beit Yosef, Orach Chayim 58:3 traces this halacha to the Gemara's dispute between Rabbi Yehoshua's position that the time runs until three hours, explaining that the halacha follows Rabbi Yehoshua, and that authorities debated whether this means the beginning or end of the third hour, concluding it means the end of the third hour.
Shenei Luchot HaBerit, Aseret HaDibrot, Tamid, Ner Mitzva:93 warns practically that lengthy melodies and piyutim, especially on short winter days, can cause people to pass the proper time for Shema, and rules that once the time has fully passed one may no longer recite the brachot, since doing so would constitute a brachah levatala.
Rav Eliezer Melamed (Peninei Halakhah, Prayer 11:11) frames the practical halacha today, noting that most poskim follow the Gra's three-hour reckoning from dawn but that, because the mitzvah of Shema is biblical, it is proper to follow the stricter view of the Magen Avraham, while those who follow the Gra's custom are not to be protested; he also notes that if the third hour passes, one may still recite Shema with its brachot through the fourth hour, earning reward only as one who reads Torah.
Rav Eliezer Melamed (Peninei Halakhah, Prayer 11:8) addresses the extenuating circumstance of a traveler, ruling that Birkot Kriyat Shema may be said from alot hashachar only when there is no possibility of saying them later at misheyakir, since one should not advance the brachot prematurely if the proper time can still be reached.
Tzitz Eliezer 7:4 addresses the practice of reciting Kriyat Shema before prayer on a conditional basis: if the later recitation with its brachot will fall after the accepted time, the earlier reading is counted as fulfilling the mitzvah, but if the later recitation will still be within the proper time, the earlier reading does not count, showing that the obligation to say Shema with its brachot within the proper time governs which recitation is operative.
Minchas Yitzchak 9:10 takes up the specific question of whether Kriyat Shema must be completed before sunrise, and concludes that one may read all three parshiyot before sunrise with intent to fulfill the mitzvah and then repeat them afterward with their brachot while preserving semichat ge'ula l'tefillah, though he also records the opposing view that it is preferable to recite Shema with its brachot only after sunrise.
Several sources round out the practical texture of this question: Shulchan Arukh, Orach Chayim 60:2-3 rules that one who recited Shema without a brachah has nonetheless fulfilled the mitzvah of Shema itself and need only go back to say the brachot, Arukh HaShulchan, Orach Chaim 236:13 discusses prioritizing communal prayer over semichat ge'ula when one arrives at a point where the tzibbur is already praying, and Rav Mordechai Eliyahu (Shut HaRav HaRashi 10:3) rules that the brachot of Kriyat Shema may not be recited outside their proper tefillah time, since doing so is considered a brachah levatala and would not exempt one from reciting them again within the proper time.