The concept of positive welfare is an expansion of the traditional understanding that animal welfare is defined by minimizing stress, pain, suffering, and disease. Positive welfare shifts the animal welfare narrative from a focus on reducing negative experiences to proactively providing animals with opportunities to have positive experiences and feelings. The concept, although around for several decades, is in its infancy in terms of developing ways of assessing positive welfare on farms, especially in extensive systems, and there are challenges in the adoption of positive welfare practices and the monitoring of continuous improvement at the farm level. Using an iterative approach, this critical review aims to explore the extent to which positive welfare interventions and indicators are positioned and have been developed within the animal welfare literature for sheep. This paper critiques existing positive welfare indicators, such as choices in food and the physical environment, conspecific social synchronization, maternal bonds, intergenerational knowledge transfer, positive human–animal relationships, etc., as currently assessed by the ‘good life framework’. It also reviews the characteristics of scientific measures for (positive) affective states in the current sheep literature and their potential contribution to understanding positive welfare states in sheep. In conclusion, this paper provides recommendations for future research regarding sheep welfare.