Tackling climate change requires a rapid transition to net-zero energy systems. A variety of different technologies could contribute to this transition, and uncertainty remains over their relative role and value. A growing school of thought argues that rapid cost reductions in renewables reduce the need for carbon capture and storage (CCS) in mitigation pathways. Here we use an integrated assessment model to explore how the value of CCS is affected by cost reductions in solar photovoltaics, onshore, and offshore wind. Low-cost renewables could erode the value of CCS by 15%–96% across different energy sectors. Renewables directly compete with CCS, accelerate power sector decarbonization, and enable greater electrification of end-use sectors. CCS has greatest value and resilience to low-cost renewables in sustainable bioenergy/industrial applications, with limited value in hydrogen/electricity generation. This suggests that targeted, rather than blanket, CCS deployment represents the best strategy for achieving the Paris Agreement goals.