Accessibility is a key concept in the field of transport geography. There is a rich, though not very mature, body of literature on this topic which is largely application-driven. The focus in the literature is generally on methods and concept and/or on applications. Applications generally focus on ex ante or ex post evaluations of the implications for accessibility of (candidate) policy plans. An important question is which are the main challenges in the area of accessibility research? This paper aims to examine this question and provide a research agenda for the coming one or two decades or so. The focus is on putting relatively new topics on the agenda, rather than making suggestions for improvements of given accessibility indicators. The paper does not aim to provide a complete list, but rather proposes avenues for future research focusing on (1) indicators to express accessibility, and (2) evaluation. In the area of indicators the challenges include the impact of ICT on accessibility; the inclusion of the robustness of the transport system in indicators; comparing perceptions of accessibility and traditional accessibility indicators; the option value; and the indicators of accessibility for goods transport, air transport, and slow modes. In the area of evaluation the paper discusses the pros and cons of the logsum as an accessibility measure, ethical aspects, comparisons of accessibility indicators to evaluate a specific case, and the needs of the clients of accessibility research.