Animal communication is definitely very complex. They all have their own language and it's often not just oral.
I've read an interesting theory that cats meow a lot at us humans because they see that we don't perceive their body language well enough. Out of frustration and because they see and hear that we speak a lot they adapt.
We're not to the point where we are able to translate live human communication smoothly. Even contextual text translation is terrible (Google translate).
I guess we're a long way from being able to translate animal communication effectively but I think it's a very intersting subject.