In line with an increasing emphasis on promoting positive welfare states in animals, this review extends previous accounts of how recent affective neuroscience observations may be used to identify and then to encourage animals to engage in reward-motivated behaviours. The terms affective states or affects are used to mean the subjective experiences, feelings or emotions that may motivate animals to behave in goal-directed ways and which may accompany success or failure to achieve those goals. These motivational affects may be positive, experienced as rewarding or pleasurable, or negative, experienced as aversive or punishing. There are two overall types: homeostasis-related negative affects that reflect an animal's internal physiological state, and situation-related positive or negative affects that reflect an animal's perception of its external circumstances. The major emphasis is on positive situation-related affects, in particular those that are potentially associated with exploration, feeding and animal-to-animal affiliative behaviours. The review introduces the new concept of positive affective engagement which represents the experience animals may have when they actively respond to motivations to engage in rewarding behaviours, and it incorporates all associated affects that are positive. For example, it would represent a state of engaged aliveness that may attend an animal's goal-directed, energised exploration of and interactions with a stimulus-rich environment. It also represents some states of equally energised, highly focused predatory stalking by carnivores or the focused and engaged foraging by herbivores when they are grazing in natural environments where food sources are abundant. Positive affective engagement may also be anticipated to accompany some aspects of reciprocated affiliative interactions between animals, the dedicated maternal nurturing and care of young, the joyfulness of rough-and-tumble play, and the eroticism and orgasmic pleasures of sexual activity. It is argued that highlighting the genetically pre-programmed, affectively positive impulses to engage in reward-motivated activities such as these, and the positive affects that may attend different facets of the process, draws attention to a wider spectrum of welfare enhancing experiences than has hitherto been considered to be important to animals. These neuroscience-supported observations strengthen many prior inferences made from predominantly behaviour-based investigations of animals' preferences, aversions and priorities, the associated development of successful environmental enrichments and the inclusion of these, where practicable, in more recent codes of practice or welfare.