The growing drive towards more sustainable dietary patterns has led to an increased demand for and availability of plant-based meat analogues (PBMAs). This systematic review aims to summarize the currently available evidence from human intervention studies investigating the impact of substituting animal meat (AM) with PBMAs in adults. A total of 19 studies were included. Overall, an increase in satiety following PBMA intake was reported, albeit to different extents and not always accompanied by changes in leptin and ghrelin. PBMAs generally resulted in lower protein bioavailability and a smaller increase in plasma essential amino acids in comparison to AM. However, muscle protein synthesis and physical performance were not affected. Finally, conflicting results have been reported for other outcomes, such as pancreatic and gastrointestinal hormones, oxidative stress and inflammation, vascular function, and microbiota composition. In conclusion, we documented that the impact of substituting AM with PBMA products has been scarcely investigated. In addition, the heterogeneity found in terms of study design, population, outcomes, and findings suggests the need for additional high-quality intervention trials, particularly long-term ones, to better clarify the advantages and potential critical issues of such substitutions within sustainable healthy diets.