We discuss three interlinked issues: the natural pace of environmental change and adaptation, the likelihood that a population will adapt to a potentially lethal change, and adaptation to elevated CO₂, the prime mover of global change.1. Environmental variability is governed by power laws showing that ln difference in conditions increases with ln elapsed time at a rate of 0.3–0.4. This leads to strong but fluctuating selection in many natural populations.2. The effect of repeated adverse change on mean fitness depends on its frequency rather than its severity. If the depression of mean fitness leads to population decline, however, severe stress may cause extinction. Evolutionary rescue from extinction requires abundant genetic variation or a high mutation supply rate, and thus a large population size. Although natural populations can sustain quite intense selection, they often fail to adapt to anthropogenic stresses such as pollution and acidification and instead become extinct.3. Experimental selection lines of algae show no specific adaptation to elevated CO₂, but instead lose their carbon‐concentrating mechanism through mutational degradation. This is likely to reduce the effectiveness of the oceanic carbon pump. Elevated CO₂is also likely to lead to changes in phytoplankton community composition, although it is not yet clear what these will be.We emphasize the importance of experimental evolution in understanding and predicting the biological response to global change. This will be one of the main tasks of evolutionary biologists in the coming decade.

Marine phytoplankton have many obvious characters, such as rapid cell division rates and large population sizes, that give them the capacity to evolve in response to global change on timescales of weeks, months or decades. However, few studies directly investigate if this adaptive potential is likely to be realized. Because of this, evidence of to whether and how marine phytoplankton may evolve in response to global change is sparse. Here, we review studies that help predict evolutionary responses to global change in marine phytoplankton. We find limited support from experimental evolution that some taxa of marine phytoplankton may adapt to ocean acidification, and strong indications from studies of variation and structure in natural populations that selection on standing genetic variation is likely. Furthermore, we highlight the large body of literature on plastic responses to ocean acidification available, and evolutionary theory that may be used to link plastic and evolutionary responses. Because of the taxonomic breadth spanned by marine phytoplankton, and the diversity of roles they fill in ocean ecosystems and biogeochemical cycles, we stress the necessity of treating taxa or functional groups individually.

Summary: Rapid climate change both imposes strong selective pressures on natural populations – potentially reducing their growth rate and causing genetic evolution – and affects the physiology and development of individual organisms. Understanding and predicting the fates of populations under global change, including extinctions and geographical range shifts, requires analysing the interplay of these processes, which has long been a grey area in evolutionary biology. We review recent theory on the interaction of phenotypic plasticity, genetic evolution and demography in environments that change in time or space. We then discuss the main limitations of the models and the difficulties in testing theoretical predictions in the wild, notably regarding changes in phenotypic selection, the evolution of (co)variances of reaction norm parameters, and transient dynamics. We use two landmark examples of physiological responses to climate change –trees facing drier climate and extreme temperatures, and marine phytoplankton under rising CO₂ – to highlight relatively neglected questions and indicate the theoretical and empirical challenges that they raise. These examples illustrate notably that age‐specific patterns of plasticity and selection on the one hand, and changes in community interactions and functioning on the other hand, need to be further investigated theoretically and empirically for a better understanding of evolutionary demographic responses to climate change in the wild.