Contemporary comparative cognition has a large repertoire of animal models and methods, with concurrent theoretical advances that are providing initial answers to crucial questions about human cognition. What cognitive traits are uniquely human? What are the species-typical inherited predispositions of the human mind? What is the human mind capable of without certain types of specific experiences with the surrounding environment? Here, we review recent findings from the domains of space, time and number cognition. These findings are produced using different comparative methodologies relying on different animal species, namely birds and non-human great apes. The study of these species not only reveals the range of cognitive abilities across vertebrates, but also increases our understanding of human cognition in crucial ways.