The integration of variable renewable energies requires new and appropriate regulatory and operational frameworks to properly move towards more efficient and reliable low-carbon electricity systems. While their name implies a focus on the long run availability of power generating capacity, their true role could be much larger. Capacity markets could actually play a key role in integrating different flexibility services - including short-term demand curtailment, storage, access to interconnections, and, of course, capacity itself - in a single framework, where decisions are made at the margin according to the variable costs of different options over different time frames.