Although there have been a growing number of studies focusing on dog welfare, the research field concerning dog positive-emotion assessment remains mostly unexplored. This paper aims to provide a state-of-the-art review and summary of the scattered and disperse research on dog positive-emotion assessment. The review notably details the current advancement in dog positive-emotion research, what approaches, measures, methods, and techniques have been implemented so far in emotion perception, processing, and response assessment. Moreover, we propose possible future research directions for short-term emotion as well as longer-term emotional states assessment in dogs. The review ends by identifying and addressing some methodological limitations and by pointing out further methodological research needs.