Evolution is driven by the propagation of genes, traits and individuals within and between populations. This propagation depends on the survival, fertility and dispersal of individuals at each age or stage during their life history, as well as on population growth and (st)age structure. Demography is therefore central to understanding evolution. Recent demographic research provides new perspectives on fitness, the spread of mutations within populations and the establishment of life histories in a phylogenetic context. New challenges resulting from individual heterogeneity, and instances where survival and reproduction are linked across generations are being recognized. Evolutionary demography is a field of exciting developments through both methodological and empirical advances. Here, we review these developments and outline two emergent research questions.