Palms are integral structural and functional components of tropical forest ecosystems, and are one of the most economically important plant families. This monocotyledon lineage exhibits a pantropical distribution with approx. 2600 species. Palm genetic diversity is severely threatened by habitat degradation, fragmentation, extensive resource extraction, and the loss of mutualistic species. This genetic erosion could considerably reduce the adaptation potential and persistence of taxa under climate change, which could pervasively impact the functioning of tropical forest ecosystems. In this review, with the insight of the post-2020 Global Biodiversity Framework, which emphasizes conservation and monitoring of genetic diversity, we summarize the impacts of anthropogenic interventions on palm populations, past decades of research on conservation genetics, and propose a future course of action using genomic and epigenomic approaches to conserve palm genetic resources in the context of climate change. Anthropogenic interventions in natural habitats have considerably reduced viable populations and altered the genetic characteristics of palm populations. Populations of many species are fragmented with disturbed mating patterns owing to the loss of reproductively active individuals and dispersal agents. Furthermore, climate change is predicted to have an adverse impact on current palm distribution, and assisted migration to suitable climatic niches is recommended. In this context, the integration of phenotypic, genetic, epigenetic, and genomic approaches in congruence with bioclimatic variables can enhance the adaptive potential and climatic resilience to implement effective conservation strategies in palms.