This paper reviews studies from the past 30 years that use operations research methods to tackle containership routing and scheduling problems at the strategic, tactical, and operational planning levels. These problems are first classified and summarized, with a focus on model formulations, assumptions, and algorithm design. The paper then gives an overview of studies on containership fleet size and mix, alliance strategy, and network design (at the strategic level); frequency determination, fleet deployment, speed optimization, and schedule design (at the tactical level); and container booking and routing and ship rescheduling (at the operational level). The paper further elaborates on the needs of the liner container shipping industry and notes the gap between existing academic studies and industrial practices. Research on containership routing and scheduling lags behind practice, especially in the face of the fast growth of the container shipping industry and the advancement of operations research and computer technology. The purpose of this paper is to stimulate more practically relevant research in this emerging area.