Understanding the factors that influence the resilience of biological systems to environmental change is a pressing concern in the face of increasing human impacts on ecosystems and the organisms that inhabit them. However, most considerations of biological resilience have focused at the community and ecosystem levels, whereas here we discuss how including consideration of processes occurring at lower levels of biological organization may provide insights into factors that influence resilience at higher levels. Specifically, we explore how processes at the genomic and epigenomic levels may cascade up to influence resilience at higher levels. We ask how the concepts of "resistance," or the capacity of a system to minimize change in response to a disturbance, and "recovery," or the ability of a system to return to its original state following a disturbance and avoid tipping points and resulting regime shifts, map to these lower levels of biological organization. Overall, we suggest that substantial changes at these lower levels may be required to support resilience at higher levels, using selected examples of genomic and epigenomic responses of fish to climate-change-related stressors such as high temperature and hypoxia at the levels of the genome, epigenome, and organism.