The domestic cat (Felis silvestris catus) has shared an intertwined existence with humans for thousands of years, living on our city streets and in our homes. Yet, little scientific research has focused on the cognition of the domestic cat, especially in comparison with human's other companion, the domestic dog (Canis lupus familiaris). This review surveys the current status of several areas of cat cognition research including perception, object permanence, memory, physical causality, quantity and time discrimination, cats' sensitivity to human cues, vocal recognition and communication, attachment bonds, personality, and cognitive health. Although interest in cat cognition is growing, we still have a long way to go until we have an inclusive body of research on the subject. Therefore, this review also identifies areas where future research must be conducted. In addition to the scientific value of future work in this area, future research on cat cognition could have an important influence on the management and welfare of pet and free-roaming cats, leading to improved human-cat interactions.