Frequency-dependent (FD) selection is a central process maintaining genetic variation and mediating evolution of population fitness. FD selection has attracted interest from researchers in a wide range of biological subdisciplines, including evolutionary genetics, behavioural ecology and, more recently, community ecology. However, the implications of frequency dependence for applied biological problems, particularly maladaptation, biological conservation and evolutionary rescue remain underexplored. The neglect of FD selection in conservation is particularly unfortunate. Classical theory, dating back to the 1940s, demonstrated that frequency dependence can either increase or decrease population fitness. These evolutionary consequences of FD selection are relevant to modern concerns about population persistence and the capacity of evolution to alleviate extinction risks. But exactly when should we expect FD selection to increase versus decrease absolute fitness and population growth? And how much of an impact is FD selection expected to have on population persistence versus extinction in changing environments? The answers to these questions have implications for evolutionary rescue under climate change and may inform strategies for managing threatened populations. Here, we revisit the core theory of FD selection, reviewing classical single-locus models of population genetic change and outlining short- and long-run consequences of FD selection for the evolution of population fitness. We then develop a quantitative genetic model of evolutionary rescue in a deteriorating environment, with population persistence hinging upon the evolution of a quantitative trait subject to both frequency-dependent and frequency-independent natural selection. We discuss the empirical literature pertinent to this theory, which supports key assumptions of our model. We show that FD selection can promote population persistence when it aligns with the direction of frequency-independent selection imposed by abiotic environmental conditions. However, under most scenarios of environmental change, FD selection limits a population's evolutionary responsiveness to changing conditions and narrows the rate of environmental change that is evolutionarily tolerable.