Many attempts have been made to introduce pepinos in several countries. These efforts have involved breeding programs designed to adapt pepino plants to the respective climates and consumer preferences. However, low yields and the relatively small amount of information on the crop have played a negative role for the expansion of the pepino. Information on other features of the fruit (e.g., quality, physiology, and sensory attributes) is also scarce. Only a few studies provide useful data on pepino handling and storage potential; hence, there is not an adequate postharvest strategy to store this species. The objective of this review is to provide and discuss the available literature, with an emphasis on postharvest physiology aspects, and present 1) breeding for quality and how this has led to the development of the cultivars known today, 2) fruit physiology and quality, 3) handling and physiological disorders of pepino, and 4) highlight challenges for future research.