Rigs are critical capital-intensive resources for oil and gas exploration and production operations, such as drilling, completion, and workover. The Rig Scheduling Problem (RSP) comprises deciding which rigs will serve each of the wells and when the operations must be performed. Several studies considering the theoretical and practical perspectives of the RSP are available, but no complete literature review exists. Aiming to fill this gap, we developed an extensive and systematic literature review. We propose a classification for the RSP and examine 130 studies selected after implementing a structured search and analysis protocol. The majority of the papers surveyed consider homogeneous workover rigs for onshore wells, usually employing heuristics. Moreover, we observe a trend towards addressing more complex problems involving heterogeneous fleets and more realistic assumptions through advanced analytical methods. The opportunities for further research identified include considering uncertainty, integrating the RSP with other decisions, and validating technical developments in real instances.