In-space servicing - repair, upgrade, and maintenance - with astronauts and advanced tool systems has been successfully demonstrated since the early 1990s with the International Space Station and the Hubble Space Telescope. Likewise over the past two decades, although perhaps not as spectacularly, in-space robotic operations have become increasingly accomplished. The DARPA/Boeing Orbital Express and the first in a series of ESA Automated Transfer Vehicle missions, for example, have demonstrated that robots can carry out complex acquisition, docking, servicing, depoting, and refueling activities in low-Earth orbit. We will discuss the current and near-future state of robotic systems intended for servicing missions of various kinds, primarily from the point of view of users. In this context, an ISS-based demonstration mission may be the next step in developing on-orbit servicing capabilities. We conclude that for highly complex and contingent operation, astronaut-based servicing remains unsurpassed in a number of venues. Robot-based servicing is becoming advanced enough that it should be considered in planning for future NASA scientific missions.