These are important questions which often don't get asked because the novelty of Birkot Keriat Shema (let's acronymize that because it will come up alot: BKSh) wears off somewhat after saying them twice daily.
What exactly are they?
There are two blessings which precede the morning and evening Shema, one blessing which follows the morning Shema, and 2 (in some customs, 3) blessings which follow the evening Shema.
What exactly are they? What kind of relationship do they have with the Shema? We need to make a Beracha to make a prayer? What are we saying in the Berchot Kriat Shema?
At first glance, BKSh seem like standard Birkot HaMitzvot, blessings on the performance of Mitzvot, just like we say blessings before picking up a Lulav or hearing the Shofar blasts. However, the Mishna in Brachot (9b) rules that one can even say BKSh after the time for saying Shema has elapsed. This (and some other Gemaras) leads the Rashba (Responsa 1:47, 319) to rule that BKSh are not Birkot HaMitzvot but other Brachot which were established to be said every night and morning.
The Ramban, however, writes (Chiddushim to Brachot 11b) that everyone knows that the blessing Ahavat Olam/Ahava Rabbah (ie the second of the two initial BKSh) is a Birkat HaMitzva. He does concede that the first blessing of BKSh at night and in the morning is not a Birkat HaMitzva. For those still worried about the question of the Rashba, the Mishkenot Yaakov (80) suggests that the only permission to say BKSh after the time for Shema has elapsed is because of Tashlumin (a compensatory prayer) and if one were to say Shema on purpose without BKSh at the right time, he could not make-up the lost BKSh later. The Mishna then is only talking about where one missed saying BKSh accidentally.
As for why the Rabbis would establish BKSh to be next to Shema, it seems it is because they are thematically related. The first of BKSh relates to the time of day, the second to learning Torah (which is what Shema in a sense is), and the final one to Redemption (which is how Shema ends off).
Who composed them?
As with most fixed prayers, Rambam writes (Brachot 1:5) that Ezra and his court established the proper words to be used. The Rashba (Brachot 11a) challenges this, because if that were so, we would expect the Talmud to provide us with the exact wording, or at least mnemonics to ensure it stayed accurate, such as the number of words in each blessing. He writes that the original enactments included what the content or theme of the blessing should be and its structure (should it open with "Baruch Attah", should it have an ending blessing etc.), and the fact that our Siddurim are fixed is more a matter of very longstanding custom than authorial intent. (See also this article)