The mutualism between plants and their pollinators provides globally important ecosystem services, but it is likely to be disrupted by global warming that can cause mismatches between both halves of this interaction. In this review, we summarise the available evidence on (i) spatial or (ii) phenological shifts of one or both of the actors of this mutualism. While the occurrence of future spatial mismatches is predominantly theoretical and based on predictive models, there is growing empirical evidence of phenological mismatches occurring at the present day. Mismatches may also occur when pollinators and their host plants are still found together. These mismatches can arise due to (iii) morphological modifications and (iv) disruptions to host attraction and foraging behaviours, and it is expected that these mismatches will lead to novel community assemblages. Overall plant–pollinator interactions seem to be resilient biological networks, particularly because generalist species can buffer these changes due to their plastic behaviour. However, we currently lack information on where and why spatial mismatches do occur and how they impact the fitness of plants and pollinators, in order to fully assess if adaptive evolutionary changes can keep pace with global warming predictions.