Summary Migration is a widespread phenomenon in the animal kingdom, including many taxonomic groups and modes of locomotion. Developing an understanding of the proximate and ultimate causes for this behaviour not only addresses fundamental ecological questions but has relevance to many other fields, for example in relation to the spread of emerging zoonotic diseases, the proliferation of invasive species, aeronautical safety as well as the conservation of migrants. Theoretical methods can make important contributions to our understanding of migration, by allowing us to integrate findings on this complex behaviour, identify caveats in our understanding and to guide future empirical research efforts. Various mechanistic models exist to date, but their applications seem to be scattered and far from evenly distributed across taxonomic units. Therefore, we provide an overview of the major mechanistic modelling approaches used in the study of migration behaviour and characterize their fundamental features, assumptions and limitations and discuss their typical data requirements both for model parameterization and for scrutinizing model predictions. Furthermore, we review 155 studies that have used mechanistic models to study animal migration and analyse them with regard to the approaches used and the focal species, and also explore their contribution to advancing current knowledge within six broad migration ecology research themes. This identifies important gaps in our present knowledge, which should be tackled in future research using existing and to-be developed theoretical approaches. ; Summary Migration is a widespread phenomenon in the animal kingdom, including many taxonomic groups and modes of locomotion. Developing an understanding of the proximate and ultimate causes for this behaviour not only addresses fundamental ecological questions but has relevance to many other fields, for example in relation to the spread of emerging zoonotic diseases, the proliferation of invasive species, aeronautical safety as well as the conservation of migrants. Theoretical methods can make important contributions to our understanding of migration, by allowing us to integrate findings on this complex behaviour, identify caveats in our understanding and to guide future empirical research efforts. Various mechanistic models exist to date, but their applications seem to be scattered and far from evenly distributed across taxonomic units. Therefore, we provide an overview of the major mechanistic modelling approaches used in the study of migration behaviour and characterize their fundamental features, assumptions and limitations and discuss their typical data requirements both for model parameterization and for scrutinizing model predictions. Furthermore, we review 155 studies that have used mechanistic models to study animal migration and analyse them with regard to the approaches used and the focal species, and also explore their contribution to advancing current knowledge within six broad migration ecology research themes. This identifies important gaps in our present knowledge, which should be tackled in future research using existing and to-be developed theoretical approaches.