Practical relevance: Cats are descended from a solitary, territorial ancestor, and while domestication has reduced their inherited tendency to be antagonistic towards all animals larger than their typical prey, they still place more reliance on the security of their territory than on psychological attachments to people or other cats, the exact opposite to dogs. Many feline problem behaviours stem from perceived threats to this security, often due to conflicts with other cats. Others are more developmental in origin, often caused by inadequate exposure to crucial stimuli, especially people, during the socialisation period. Strongly aversive events experienced at any age can also contribute. A third category comprises normal behaviour that owners deem unacceptable, such as scratching of furniture. Evidence base: This review identifies three areas in which basic research is inadequate to support widely employed concepts and practices in feline behavioural medicine. First, classification of cats’ problem behaviours relies heavily on approaches derived from studies of their behavioural ecology and, to some extent, extrapolation from canine studies. Few studies have focused on cats in the home, the environment in which most behavioural disorders are expressed. Secondly, cats’ chemical senses (olfactory and vomeronasal) are far more sensitive than our own, making it difficult for owners or clinicians to fully comprehend the sensory information upon which they base their behaviour. Thirdly, although the concept of psychological distress is widely invoked as an intervening variable in behavioural disorders, there are still no reliable measures of distress for pet cats in the home. Global importance: Psychological distress of some kind is the primary cause of many of the behavioural problems presented to clinicians, but surveys indicate that many more cats display the same clinical signs without their owners ever seeking help. The welfare of this ‘invisible’ group could be improved by veterinarians taking a more proactive approach to educating their clients about the behavioural needs of pet cats.