The development of the Internet drove significant changes in the social and economic functioning of people and spatial units. In the case of geography, the Internet changed its nature as a science about space, by expanding on the available topics and methods of study by which geographers come to know the world. New possibilities were a result, though also challenges, above all in relation to the role in geographical research played by the Internet and digital space (data generated through the use of the Internet). Major developments to the World Wide Web and to the Internet as a whole, as well as new solutions made possible by the latter’s creation combine with phenomena subject to scientific analysis to leave as insufficient previous state-of-the-art research methods in the field of Internet geography. The aim of this article is therefore to identify the main problems with research in digital space. Emphasis is put on relationships between real and digital space from the two complementary perspectives of digital space as a source of information about real space for research and of digital space as the subject of research. Explored first is the way in which digital space furnishes data upon which descriptions of real space can be based. An attempt is then made to discover the nature of digital space in its spatial aspects, with the relationship between digital and real space determined. A literature review further serves as the basis for the presentation of four research topics relating to the geography of the Internet, i.e. digital-divide analysis, issues of the management of socio-economic processes, cyber-balkanisation, and the relationships between real and digital spaces. The digital divide relates to access or skills, as well as to individual motivations and socio-cultural preferences, which can also be observed in the different ways people use the Internet. The digital divide is subject to constant change amid the rapid development of the Internet and the increasing importance of the Web in everyday life. Growing interest in concepts relating to the functionality of various areas in so-called smart cities and smart rural areas arises out of issues of spatial management. Cyber-balkanisation in turn constitutes a fragmentation of the Internet more and more manifested by users as they have increased control over online content. The final research topic, concerned with the relationships between real and digital spaces, is crucial to an understanding of the Internet’s role in geography. The presented areas of research on the Internet and digital space, as well as the research directions referred to, should be treated as a starting point for a broader discussion. In the case of analyses of Internet geography, it is essential for basic terms to be determined and defined. Also of importance is a general determination of the role and importance of the Internet in geography.