Species’ distributions, population sizes, and community composition are affected, directly and indirectly, by climatic changes, leading to changes in location, extent, and/or quality of distributions, range fragmentation or coalescence, and temporal discontinuities in suitable conditions. Quaternary fossil records document these responses, emphasizing individualism of species’ responses and impermanence of communities. Recent observations document similar changes attributable to recent climatic changes, including rapid decreases and increases in ranges and/or populations. Both also document extinctions associated with rapid climatic changes. Modelling studies predict substantial changes in species’ distributions, population sizes, and communities in response to future climatic changes. Implicit assumptions that genetic variation enabling adaptation is ubiquitous throughout species’ ranges, or that gene flow may be sufficiently rapid to allow adaptation, may be invalid. Work is needed to investigate spatial structuring of adaptive genetic variation and rates of gene flow, and to develop new models. Without this, species extinction risks may be severely underestimated.