Why and how new migration routes emerge remain fundamental questions in ecology, particularly in the context of current global changes. In its early stages, when few individuals are involved, the evolution of new migration routes can be easily confused with vagrancy, i.e. the occurrence of individuals outside their regular breeding, non-breeding or migratory distribution ranges. Yet, vagrancy can in theory generate new migration routes if vagrants survive, return to their breeding grounds and transfer their new migration route to their offspring, thus increasing a new migratory phenotype in the population. Here, we review the conceptual framework and empirical challenges of distinguishing regular migration from vagrancy in small obligate migratory passerines and explain how this can inform our understanding of migration evolution. For this purpose, we use the Yellow-browed Warbler (Phylloscopus inornatus) as a case study. This Siberian species normally winters in southern Asia and its recent increase in occurrence in Western Europe has become a prominent evolutionary puzzle. We first review and discuss available evidence suggesting that the species is still mostly a vagrant in Western Europe but might be establishing a new migration route initiated by vagrants. We then list possible empirical approaches to check if some individuals really undertake regular migratory movements between Western Europe and Siberia, which would make this species an ideal model for studying the links between vagrancy and the emergence of new migratory routes.