Evolutionary changes are determined by a complex assortment of ecological, demographic, and adaptive histories. Predicting how evolution will shape the genetic structures of populations coping with current (and future) environmental challenges has principally relied on investigations through space, in lieu of time, because long-term phenotypic and molecular data are scarce. Yet, dormant propagules in sediments, soils, and permafrost are convenient natural archives of population histories from which to trace adaptive trajectories along extended time periods. DNA sequence data obtained from these natural archives, combined with pioneering methods for analyzing both ecological and population genomic time-series data, are likely to provide predictive models to forecast evolutionary responses of natural populations to environmental changes resulting from natural and anthropogenic stressors, including climate change.