There is a significant amount of synergy between virtual reality (VR) and the field of robotics. However, it has only been in approximately the past five years that commercial immersive VR devices have been available to developers. This new availability has led to a rapid increase in research using VR devices in the field of robotics, especially in the development of VR interfaces for operating robots. In this paper, we present a systematic review on VR interfaces for robot operation that utilize commercially available immersive VR devices. A total of 41 papers published between 2016–2020 were collected for review following the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. Papers are discussed and categorized into five categories: (1) Visualization, which focuses on displaying data or information to operators; (2) Robot Control and Planning, which focuses on connecting human input or movement to robot movement; (3) Interaction, which focuses on the development of new interaction techniques and/or identifying best interaction practices; (4) Usability, which focuses on user experiences of VR interfaces; and (5) Infrastructure, which focuses on system architectures or software to support connecting VR and robots for interface development. Additionally, we provide future directions to continue development in VR interfaces for operating robots.