Alternative proteins are receiving increased global attention. This burgeoning interest in plants (especially plant-based meat alternatives), insects, algae, and cultured meat has been attributed to their reported health benefits, lower environmental impact and improved animal welfare compared to conventional animal-based meat. Food producers and the media are promoting acceptance of these products, claiming superior nutritional, environmental and ethical credentials and a desirable novel sensory experience. However, the evidence supporting these claims remains unclear. In this review, we summarise the main evidence underlying the nutritional, sensorial, economical, ethical, and environmental reasons reported for the rise in consumer demand for alternative proteins. We found many of these reasons to lack a strong evidence base. For instance, evidence is emerging for the nutritional benefits of plant-based meat alternatives, but present claims are largely based on established evidence for plant-based diets. Significant research gaps remain, especially longitudinal evidence on the sustained effects of replacing conventional animal-based proteins with alternative sources. For many alternative proteins, challenges exist in achieving desirable sensory properties akin to animal-based meat to promote their acceptance by consumers. Overall, fundamental shifts in the food system are required to create a culture in which healthful and sustainable food choices are the norm.