Reward is a concept fundamental to discussions of drug abuse and addiction. The idea that altered sensitivity to either drug-reward, or to rewards in general, contributes to, or results from, drug-taking is a common theme in several theories of addiction. However, the concept of reward is problematic in that it is used to refer to apparently different behavioural phenomena, and even to diverse neurobiological processes (reward pathways). Whether these different phenomena are different behavioural expressions of a common underlying process is not established, and much research suggests that there may be only loose relationships among different aspects of reward. Measures of rewarding effects of drugs in humans often depend upon subjective reports. In animal studies, such insights are not available, and behavioural measures must be relied upon to infer rewarding effects of drugs or other events. In such animal studies, but also in many human methods established to objectify measures of reward, many other factors contribute to the behaviour being studied. For that reason, studying the biological (including genetic) bases of performance of tasks that ostensibly measure reward cannot provide unequivocal answers. The current overview outlines the strengths and weaknesses of current approaches that hinder the conciliation of cross-species studies of the genetics of reward sensitivity and the dysregulation of reward processes by drugs of abuse. Some suggestions are made as to how human and animal studies may be made to address more closely homologous behaviours, even if those processes are only partly able to isolate 'reward' from other factors contributing to behavioural output.