Landscape connectivity, the extent to which a landscape facilitates the flow of ecological processes such as organism movement, has emerged as a central focus of landscape ecology and conservation science. Connectivity modelling now encompasses an enormous body of work across ecological theory and application. The dominant connectivity models in use today are based on the framework of ‘landscape resistance’, which is a way of measuring how landscape structure influences movement patterns. However, the simplistic assumptions and high degree of reductionism inherent to the landscape resistance paradigm severely limits the ability of connectivity algorithms to account for many fundamental aspects of animal movement, and thus greatly reduces the effectiveness and relevance of connectivity models for conservation theory and practice. In this paper, we first provide an overview of the development of connectivity modelling and resistance surfaces. We then discuss several key drivers of animal movement which are absent in resistance-based models, with a focus on spatiotemporal variation, human and interspecies interactions, and other context-dependent effects. We look at a range of empirical studies which highlight the strong impact these effects have on movement and connectivity predictions. But we also provide promising avenues of future research to address this: we discuss newly emerging technologies and interdisciplinary work, and look to developing methodologies, models and conversations which move beyond the limiting framework of landscape resistance, so that connectivity models can better reflect the complexities and richness of animal movement.