The measurement of how people are "exposed" to media content, which is crucial for the understanding of media use and effects, has been a challenge for a long time. Today's media landscape, in which individuals are exposed to a diversity of messages anytime, anywhere, and from a great variety of sources on an increasing number of different media platforms, has complicated the measurement of media exposure even more. However, today's digital media landscape also offers new possibilities to map media exposure by means of passive measurement. In this Introduction article to the special issue, we give an overview of the different ways in which media exposure is measured and the various issues associated with their applications. We conclude with a research agenda for issues that need to be tackled in future research and also introduce a research tool for media exposure measurement.