Artificial intelligence (AI) and cognitive science have different aims. AI has two overlapping, mutually supporting strands, namely science concerned with understanding what is and is not possible in natural and artificial intelligent systems, and engineering concerned mainly with producing new useful kinds of machines. Cognitive science and cognitive modeling overlap significantly with the science strand of AI. However, the majority of AI researchers have a strong engineering orientation. In contrast, those who were responsible for many of the key ideas in AI were all interested in AI primarily as a contribution to the general science of mind. Early AI researchers discovered that combinatorial explosions threatened progress in AI psychology. This chapter has reviewed some gaps that still need to be filled, outlining some ways of accelerating progress toward the development of models that are more human-like, using deeper and more comprehensive theories of human and animal cognitive competences.