Summary: Climate refugia, locations where taxa survive periods of regionally adverse climate, are thought to be critical for maintaining biodiversity through the glacial–interglacial climate changes of the Quaternary. A critical research need is to better integrate and reconcile the three major lines of evidence used to infer the existence of past refugia – fossil records, species distribution models and phylogeographic surveys – in order to characterize the complex spatiotemporal trajectories of species and populations in and out of refugia. Here we review the complementary strengths, limitations and new advances for these three approaches. We provide case studies to illustrate their combined application, and point the way towards new opportunities for synthesizing these disparate lines of evidence. Case studies with European beech, Qinghai spruce and Douglas‐fir illustrate how the combination of these three approaches successfully resolves complex species histories not attainable from any one approach. Promising new statistical techniques can capitalize on the strengths of each method and provide a robust quantitative reconstruction of species history. Studying past refugia can help identify contemporary refugia and clarify their conservation significance, in particular by elucidating the fine‐scale processes and the particular geographic locations that buffer species against rapidly changing climate. Contents Summary 38 I. Climate refugia: biogeographical and conservation significance 38 II. Approaches for reconstructing refugia: strengths, limitations and recent advances 39 III. Climate refugia of the past: three case studies 46 IV. New integrative approaches to reconstructing refugia 47 V. How can historical refugia inform us about future refugia? 48 VI. Concluding thoughts 49 Acknowledgements 49 References 49

Persistence of natural populations during periods of climate change is likely to depend on migration (range shifts) or adaptation. These responses were traditionally considered discrete processes and conceptually divided into the realms of ecology and evolution. In a milestone paper, Davis and Shaw (2001)Science292:673 argued that the interplay of adaptation and migration was central to biotic responses to Quaternary climate, but since then there has been no synthesis of efforts made to set up this research program. Here we review some of the salient findings from molecular genetic studies assessing ecological and evolutionary responses to Quaternary climate change. These studies have revolutionized our understanding of population processes associated with past species migration. However, knowledge remains limited about the role of natural selection for local adaptation of populations to Quaternary environmental fluctuations and associated range shifts, and for the footprints this might have left on extant populations. Next‐generation sequencing technologies, high‐resolution paleoclimate analyses, and advances in population genetic theory offer an unprecedented opportunity to test hypotheses about adaptation through time. Recent population genomics studies have greatly improved our understanding of the role of contemporary adaptation to local environments in shaping spatial patterns of genetic diversity across modern‐day landscapes. Advances in this burgeoning field provide important conceptual and methodological bases to decipher the historical role of natural selection and assess adaptation to past environmental variation. We suggest that a process called “temporal conditional neutrality” has taken place: some alleles favored in glacial environments become selectively neutral in modern‐day conditions, whereas some alleles that had been neutral during glacial periods become under selection in modern environments. Building on this view, we present a new integrative framework for addressing the interplay of demographic and adaptive evolutionary responses to Quaternary climate dynamics, the research agenda initially envisioned by Davis and Shaw (2001)Science292:673.