Biological invasions are a major challenge to native communities and have the potential to exert strong selection on native populations. As a result, native taxa may adapt to the presence of invaders through increased competitive ability, increased antipredator defences or altered morphologies that may limit encounters with toxic prey. Yet, in some cases, species may fail to adapt to biological invasions. Many challenges to adaptation arise because biological invasions occur in complex species-rich communities in spatially and temporally variable environments. Here, we review these ‘ecological’ constraints on adaptation, focusing on the complications that arise from the need to simultaneously adapt to multiple biotic agents and from temporal and spatial variation in both selection and demography. Throughout, we illustrate cases where these constraints might be especially important in native populations faced with biological invasions. Our goal was to highlight additional complexities empiricists should consider when studying adaptation to biological invasions and to begin to identify conditions when adaptation may fail to be an effective response to invasion.