Virtual reality (VR) has emerged as a powerful tool for rehabilitation. Many effective VR applications have been developed to support motor rehabilitation of people affected by motor issues. Movement reproduction, which transfers users' movements from the physical world to the virtual environment, is commonly used in VR rehabilitation applications. Three major components are required for movement reproduction in VR: (1) movement input, (2) movement representation, and (3) movement modulation. Until now, movement reproduction in virtual rehabilitation has not yet been systematically studied. This article aims to provide a state-of-the-art review on this subject by focusing on existing literature on immersive motor rehabilitation using VR. In this review, we provided in-depth discussions on the rehabilitation goals and outcomes, technology issues behind virtual rehabilitation, and user experience regarding movement reproduction. Similarly, we present good practices and highlight challenges and opportunities that can form constructive suggestions for the design and development of fit-for-purpose VR rehabilitation applications and can help frame future research directions for this emerging area that combines VR and health.