We are commanded to set aside all male firstborn of humans, clean animals, and asses, as it says "Sanctify to Me every firstborn of the children of Israel, everything that opens the womb of man and of animal".¹ Human and asses' firstborn are redeemed and their redemption price belongs to the priests; but the firstborn of a clean animal cannot be redeemed -- it is offered as a sacrifice and the priests eat its flesh in Jerusalem, as it says "[And Ha-Shem said to Aaron... everything that opens the womb... of man and animal shall be yours;] but you shall redeem the human firstborn and the firstborn of the unclean animal you shall redeem... but a firstborn ox or firstborn sheep or firstborn goat you shall not redeem; they are holy... and their flesh shall be yours"²; [and it says "You must not eat in your gates... the firstborn of your cattle and flocks... rather, before Ha-Shem your G-d you shall eat it..."³]. If it cannot be offered as a sacrifice because of a blemish it still belongs to the priests, as it says "[Every firstborn that is born in your sheep and cattle you shall declare holy to Ha-Shem your G-d... before Ha-Shem your G-d you shall eat it...] but if it has a blemish... you shall not sacrifice it to Ha-Shem your G-d; you shall eat it in your gates...".⁴ This commandment applies even when the Temple does not exist, in which case nothing can be done with a firstborn that has no blemish.^a

We are commanded to set aside one out of every ten cattle, sheep or goats that are born in our possession each year, and it is forbidden to redeem them, as it says "And all tithes of cattle and flocks... the tenth shall be holy to Ha-Shem... it shall not be redeemed".⁵ The sages instituted that this not be done when the Temple does not exist. It is offered as a sacrifice and the owner eats its flesh in Jerusalem; if it has a blemish it can be eaten anywhere.^b

Sources:
1. Ex. 13:2	a. 1:1-5,10,17
2. Num. 18:15-18	b. 6:1-2,4
3. Deut. 12:17-18
4. Deut. 15:19,21
5. Lev. 27:32-33