Electricity and water systems are inextricably linked through water demands for energy generation, and through energy demands for using, moving, and treating water and wastewater. Climate change may stress these interdependencies, together referred to as the energy-water nexus, by reducing water availability for hydropower generation and by increasing irrigation and electricity demand for groundwater pumping, among other feedbacks. Further, many climate adaptation measures to augment water supplies - such as water recycling and desalination - are energy-intensive. However, water and electricity system climate vulnerabilities and adaptations are often studied in isolation, without considering how multiple interactive risks may compound. This paper reviews the fragmented literature and develops a generalized framework for understanding these implications of climate change on the energy-water nexus. We apply this framework in a case study to quantify end-century direct climate impacts on California's water and electricity resources and estimate the magnitude of the indirect cross-sectoral feedback of electricity demand from various water adaptation strategies. Our results show that increased space cooling demand and decreased hydropower generation are the most significant direct climate change impacts on California's electricity sector by end-century. In California's water sector, climate change impacts directly on surface water availability exceed demand changes, but have considerable uncertainty, both in direction and magnitude. Additionally, we find that the energy demands of water sector climate adaptations could significantly affect California's future electricity system needs. If the worst-case water shortage occurs under climate change, water-conserving adaptation measures can provide large energy savings co-benefits, but other energy-intensive water adaptations may double the direct impacts of climate change on the state's electricity resource requirement. These results highlight the value of coordinated adaptation planning between the energy and water sectors to achieve mutually beneficial solutions for climate resilience.