In virtual reality, users are typically represented by and interact through a virtual body. Research frequently manipulates different features of these bodies. We analyze 208 studies to identify what aspects of virtual bodies are manipulated, how these manipulations affect interaction and other outcomes, and why they are assumed to do so. Based on the analysis, we propose a design space comprising seven types of visual manipulations: appearance, size, morphology, viewpoint, transfer, remapping, and control. We also synthesize findings on their effects—ranging from task performance to physiological responses and social outcomes—and examine the theories used to explain them, such as embodiment, Proteus effect, and presence. The design space helps researchers identify key variables and their interconnections in design and empirical research of virtual bodies. The synthesis further reveals unexplored causal connections and highlights theories that may account for observed effects.