Assisted colonisation has received considerable attention recently, and the risks and benefits of introducing taxa to sites beyond their historical range have been vigorously debated. The debate has primarily focused on using assisted colonization to enhance the persistence of taxa that would otherwise be stranded in unsuitable habitat as a consequence of anthropogenic climate change and habitat fragmentation. However, a complementary motivation for assisted colonisation could be to relocate taxa to restore declining ecosystem processes that support biodiversity in recipient sites. We compare the benefits and risks of species introductions motivated by either goal, which we respectively term 'push' versus 'pull' strategies for introductions to preserve single species or for restoration of ecological processes. We highlight that, by focusing on push and neglecting pull options, ecologists have greatly under-estimated potential benefits and risks that may result from assisted colonisation. Assisted colonisation may receive higher priority in climate change adaptation strategies if relocated taxa perform valuable ecological functions (pull) rather than have little collateral benefit (push). Potential roles include enhancing resistance to invasion by undesired species, supporting co-dependent species, performing keystone functions, providing temporally critical resources, replacing taxa of low ecological redundancy, and avoiding time lags in the provisioning of desired functions.