Gemara

70b (R. Yonason citing R. Yishmael): "When an animal will die" refers to a Tamei animal. "That you may eat" refers to a Tahor animal. Tahor and Tamei Chayos (wild animals) are included in 'Behemah' (domestic animal), and vice-versa.

"This is the Behemah that you will eat - an ox, a sheep... a deer..." teaches that 'Behemah' includes Chayah. "This is the Chayah that you will eat, from every Behemah on the ground..." teaches that 'Chayah' includes Behemah.

'Behemah' includes Tahor Chayos regarding Simanim (if it has split hooves that chews the cud, it is Kosher). 'Behemah' includes (even) Tamei Chayos for the prohibition to crossbreed different species. 'Chayah' includes Tamei Behemos for Rebbi's law;

(Beraisa - Rebbi): 'Behemah' in the Parshah of Tumos is extra (since it already said Chayah), to teach from another place that Behemah Teme'ah is mentioned, that one who became Tamei must bring a Korban only if he entered the Mikdash or ate Kodshim when Tamei.

'Chayah' includes (even) Tahor Behemos in the Parshah of creation;

(Mishnah - R. Meir): If a woman miscarried the form of a Tahor or Tamei Behemah, Chayah or bird, she has Tum'as Yoledes;

Chachamim say, only a human form is considered a child.

According to Chachamim, the rule that Chayah includes Tahor Behemos is needed for Rebbi's teaching.

84a - Question (Yakov Mina'ah): The Torah gives Simanim of Kosher Behemos, they also apply to Chayos. We should say that the Torah commands to cover the blood of Chayos, and this applies also to Behemos!

Answer (Rava): "On the ground you will spill it (blood of Pesulei ha'Mukdashim (blemished Korbanos that were redeemed, which are Behemos) like water" - just like water need not be covered, also Dam Behemah.

102a (Beraisa - R. Elazar): "Do not eat the blood, for the blood is the soul; do not eat the soul with the flesh" applies to Behemos, Chayos and birds, both Tehorim and Teme'im, i.e. everything whose blood is forbidden;

Chachamim expound "do not eat the soul with the flesh", rather, eat the flesh alone. This discusses things whose flesh is permitted, i.e. Tehorim;

R. Meir says, it applies only to Behemos Tehoros.

(Rabah bar Shmuel): R. Meir learns from a previous verse "from your cattle and flock" that this applies only to Behemos.

Bava Kama 54b (Mishnah): The following apply to all Behemos, Chayos and fowl. Falling into a pit... the double payment of a thief; returning a lost animal; unloading an animal; muzzling an animal; working with or crossbreeding diverse species; making it work on Shabbos.

The Torah said 'ox' or 'donkey', for this is the usual case.

Rishonim

Ba'al ha'Ma'or (Chulin 24b, DH Havah): In the verse "this is the Chayah that you will eat..." Chayah does not really refer to wild animals. It refers to (fully) living, and excludes Tereifos. Even so, this applies also to Behemos. Really, even without this, "Basar b'Sadeh Tereifah Lo Sochelu" forbids Stam Tereifos, i.e. Behemos and Chayos. Our Gemara merely lists all places in which 'Chayah' includes Behemah.

Tosfos ha'Rosh (Chulin 71a DH ul'Rabanan): According to Chachamim of R. Meir, 'Behemah is included in Chayah' is needed only for Rebbi's teaching. In truth, it teaches only about Teme'os.

Rambam (5:1): Ever Min ha'Chai is forbidden in Tahor Behemos, Chayos and birds.

Rambam (6:1): The Torah forbids blood of "Ohf and Behemah", and Behemah includes Chayah. One is not liable for blood of fish and Chagavim (grasshoppers or locusts). Therefore, one may eat the blood of Tahor fish and Chagavim, even if it is gathered in a Keli.

Ra'avad: Chachamim forbade the blood if it is gathered, due to suspicion, unless there are scales in it (to prove that it is from Tahor fish).

Rambam (Hilchos Shechitah 1:1): It is a Mitzvas Aseh that one who wants to eat meat of a Behemah, Chayah or bird must slaughter and afterwards eat, for it says "you will slaughter from your cattle and flock." It says about a blemished Bechor "like you will eat a deer or wild goat." This teaches that Chayos are included in Behemos regarding slaughter.

Magid Mishneh: Even though Chayos are included in Behemos, we needed a Hekesh, for the Torah said to slaughter cattle and flock. It did not say to slaughter Behemos.

Radvaz: Also, "v"Zovachta" refers to Kodshim. We cannot learn from it to Chayos, which cannot be Korbanos.

The Rosh (Chulin 7:39) brings the Beraisa with the three opinions about Ever Min ha'Chai.

Ma'adanei Yom Tov (100): Also Chachamim must expound "do not eat the blood..." to teach that Ever Min ha'Chai applies only to things whose blood is forbidden, i.e. Behemos, Chayos and birds, but not fish and Chagavim. The Levush (YD 62:1) says that Ever Min ha'Chai applies to Behemos, Chayos and birds, because all of them have a Nefesh. If so, even fish and Chagavim should be included.

Divrei Chamudos (187): The Rambam permits Ever Min ha'Chai of fish and Chagavim. However, Bal Teshaktzu (do not make yourselves detestable) applies.

Poskim

Shulchan Aruch (YD 30:1): If the skull of a Behemah or Chayah was battered, it is Tereifah.

Gra (1): We learn that Behemah is included in Chayah from "this (is the Chayah)", from which we learn Tereifos. Therefore, whenever something makes a Behemah Tereifah, the same applies to a Chayah.

Shulchan Aruch (39:1): One need not check for any Tereifah, except for the lungs.

Beis Yosef (DH Kosav Mahari): There was a place where they checked only Behemos, but not Chayos. Mahari ben Lev said that this is totally wrong. The Ramban says that the Torah taught primary about Treifos in Chayos, just we include Behemos! Rivash (77) says that it is obvious that a Chayah must be checked. The Tur says similarly in the name of Ba'al ha'Itur, and the Rambam agrees.

Shulchan Aruch (62): Ever Min ha'Chai is forbidden in Behemos, Chayos and birds.

Shulchan Aruch (66:1): Blood of Behemos, Chayos and birds is forbidden. Blood of fish and Chagavim is permitted.

Bach (2): The Tur teaches that one is liable for blood of Behemos, Chayos and birds, whether Tamei or Tahor. Even though in any case one may not eat anything from Tamei animals, this is relevant to mixtures. If blood of a Tamei animal was mixed with blood of Tahor fish and Chagavim (which is permitted), since the Tamei blood is forbidden, it is called blood, and the mixture is considered Min b'Mino (the same type), and any amount forbids according to Rashi. If there was no Chiyuv for Tamei blood, it would not be considered blood (rather, just part of a Tamei species), and the mixture would be considered Min b'Eino Mino (diverse types), and the Tamei blood would be Batel if there were 60 times as much permitted blood.

Pri Megadim (Sifsei Da'as 1): In any case, it is called blood, and this is Min b'Mino. Also, the Halachah does not follow Rashi. Rather, this is relevant only regarding whom is suspected about Aveiros, and vows. If so, the Mechaber should have brought it also regarding Ever Min ha'Chai!

Shulchan Aruch (79:1): Simanim of Behemos and Chayos are explicit in the Torah.

Shulchan Aruch (80:1): Chelev of a Tahor Chayah is permitted. Its blood must be covered.