Kinematic design is a predominant phase in the design of robotic manipulators for minimally invasive surgery (MIS). However, an extensive overview of the kinematic design issues for MIS robots is not yet available to both mechanisms and robotics communities. Hundreds of archival reports and articles on robotic systems for MIS are reviewed and studied. In particular, the kinematic design considerations and mechanism development described in the literature for existing robots are focused on. The general kinematic design goals, design requirements, and design preferences for MIS robots are defined. An MIS-specialized mechanism, namely the remote center-of-motion (RCM) mechanism, is revisited and studied. Accordingly, based on the RCM mechanism types, a classification for MIS robots is provided. A comparison between eight different RCM types is given. Finally, several open challenges for the kinematic design of MIS robotic manipulators are discussed. This work provides a detailed survey of the kinematic design of MIS robots, addresses the research opportunity in MIS robots for kinematicians, and clarifies the kinematic point of view to MIS robots as a reference for the medical community.