This paper reviews how the concept of Media Crossing has contributed to the advancement of the application domain of information access and explores directions for a future research agenda. These will include themes that could help to broaden the scope and to incorporate the concept of medium-crossing in a more general approach that not only uses combinations of medium-specific processing, but that also exploits more abstract medium-independent representations, partly based on the foundational work on statistical language models for information retrieval. Three examples of successful applications of media crossing will be presented, with a focus on the aspects that could be considered a first step towards a generalized form of media mining