The presence of individuals on the ground is a crucial element in domestic and conventional international taxation rules. Moreover, these rules assume that individuals and the labor factor in general have minimal international mobility. The digitalization of work challenges the paradigm of individuals' limited mobility and, consequently, threatens the proper functioning of the taxation rules on which it is based. In this context, this introductory lecture aims to: (1) Verify the dimension of post-pandemic cross-border mobility by studying, as far as possible, its relevance and essential characteristics (e.g., the phenomena of digital nomadism and whole/part-time cross-border commuting); (2) Analyze how these mobility phenomena affect the current domestic and conventional rules of international taxation and, in particular, those defining residence (of individuals and corporations), the concept of Permanent Establishment, and the source rules concerning types of income normally obtained by individuals (independent personal services, income from employment and pensions). (3) To study the various existing proposals to deal with the problems posed by applying the current rules as analyzed in (2).