Discussion this subject is frequently confused by the fact that some schools of philosophy and psychology would question whether we need to, or should, ascribe mind to any human being other than ourselves (or even to ourselves). Such an approach (for example radical behaviorism) would naturally deny the existence of animal minds as well.
However, if we accept that it is essential to talk about the minds of other humans, it remains an open question whether we can talk about animal minds in the same way. The answer obviously depends partly on how we define mind. In practice the debate focuses on a few questions within the field of animal cognition, particularly the questions of consciousness, self-concept, theory of mind and tactical deception in animals.