I recently finished the book Baboon Metaphysics, that my girlfriend's parents gave me last Christmas. They know I love anything about monkeys. The book details some of the field studies of communication that goes on between baboons, as well as other primates.
I think the line between animal communication & human language is a fuzzy one, arbitrarily delineated by us humans. Although they don't have grammar and sentence structure, animals are clearly communicating complex ideas.
Chimps & other animals have been proven to be highly intelligent, even surpassing humans in some ways.
It is interesting that animals were trained to understand human language, and only now are we beginning to unlock the meaning in animal socializing.
Perhaps one day there will be a way to achieve a fluid understanding between humans & other living things. This will greatly increase the empathy that people have for Life, in all forms.