Abstract: Comparative cognition is an emerging interdisciplinary field with contributions from comparative psychology, cognitive/experimental and developmental psychology, animal learning, and ethology, and is poised to move toward greater understanding of animal and human information-processing, reasoning, memory, and the phylogenetic emergence of mind. This chapter highlights some current issues and discusses four areas within comparative cognition that are yielding new approaches and hypotheses for studying basic conceptual capacities in nonhuman species. These include studies of imitation, tool use, mirror self-recognition, and the potential for attribution of mental states by nonhuman animals. Though a very old question in psychology, the study of imitation continues to provide new avenues for examining the complex relationships among and between the levels of imitative behaviors exhibited by many species. Similarly, recent work in animal tool use, mirror self-recognition (with all its contentious issues), and recent attempts to empirically study the potential for attributional capacities in nonhumans, all continue to provide fresh insights and novel paradigms for addressing the defining characteristics of these complex phenomena.