Demand for plant-based meat alternatives has increased in recent years due to concerns about health, ethics, the environment, and animal welfare. Nevertheless, the market share of plant-based meat alternatives must increase significantly if they are to support sustainable food production and consumption. Flavor is an important limiting factor of the acceptability and marketability of plant-based meat alternatives. Undesirable chemosensory perceptions, such as a beany flavor, bitter taste, and astringency, are often associated with plant proteins and products that use them. This study reviewed 276 articles to answer the following five research questions: (1) What are the volatile and nonvolatile compounds responsible for off-flavors? (2) What are the mechanisms by which these flavor compounds are generated? (3) What is the influence of thermal extrusion cooking (the primary structuring technique to transform plant proteins into fibrous products that resemble meat in texture) on the flavor characteristics of plant proteins? (4) What techniques are used in measuring the flavor properties of plant-based proteins and products? (5) What strategies can be used to reduce off-flavors and improve the sensory appeal of plant-based meat alternatives? This article comprehensively discusses, for the first time, the flavor issues of plant-based meat alternatives and the technologies available to improve flavor and, ultimately, acceptability.