This chapter discusses the issues and challenges arising when building a general spatio-temporal ontology for representing and reasoning of geographical processes as part of a desired universal semantic reference system of geographic space. It examines the foundations and formalisms upon which the development of such an ontological model of geographical processes can be based. The chapter begins by providing a background of essential concepts related to the representation of geographical processes. Then overviews of several approaches to representing spatio-temporal processes and how to associate them with geographic space are given. Following this, the chapter discusses several open issues on the topic and presents a set of desiderata for representing and reasoning about real-world dynamic geographical phenomena. This discussion covers aspects of space, time, object, event, state, and process as the essential concepts to represent geo-processes. It also covers aspects of spatial-temporal granularity and spatio-temporal aggregation, describing how they relate to geographical processes. Finally, this chapter also explores the phenomenon of vagueness and how it affects the representation and reasoning about geo-processes. The chapter concludes by indicating directions for future research and recapitulating its overall coverage.