Breeding is a confirmed upcoming feature of the game that lets players breed creatures using Dinosaur Eggs. Little has been confirmed other than the fact that baby creatures "will grow dynamically in real-time." The breeding will "probably" be released "before Halloween."[1]
Eggs will not have an owner until hatched, so it's possible to steal other player's eggs. Once hatched dinos can simply be claimed and do not require the traditional violent taming.[2]
In a Steam thread asking if breeding was possible, game developer Drake simply mentioned "genetic recombination" without any other context, so it's possible that players may be able to combine traits between a species.[3]