Concentrating solar power (CSP) capacity has expanded slower than other renewable technologies and its costs are still high. Until now, there have been too few CSP projects to derive robust conclusions about its cost development. Here we present an empirical study of the cost development of all operating CSP stations and those under construction, examining the roles of capacity growth, industry continuity, and policy support design. We identify distinct CSP expansion phases, each characterized by different cost pressure in the policy regime and different industry continuity. In 2008–2011, with low cost pressure and following industry discontinuity, costs increased. In the current phase, with high cost pressure and continuous industry development, costs decreased rapidly, with learning rates exceeding 20%. Data for projects under construction suggest that this trend is continuing and accelerating. If support policies and industrial structure are sustained, we see no near-term factors that would hinder further cost decreases.