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Photovoltaic (PV) conversion of solar energy starts to give an appreciable contribution to power generation in many countries, with more than 90% of the global PV market relying on solar cells based on crystalline silicon (c-Si). The current efficiency record of c-Si solar cells is 26.7%, against an intrinsic limit of ~29%. Current research and production trends aim at increasing the efficiency, and reducing the cost, of industrial modules. In this paper, we review the main concepts and theoretical approaches that allow calculating the efficiency limits of c-Si solar cells as a function of silicon thickness. For a given material quality, the optimal thickness is determined by a trade-off between the competing needs of high optical absorption (requiring a thicker absorbing layer) and of efficient carrier collection (best achieved by a thin silicon layer). The efficiency limits can be calculated by solving the transport equations in the assumption of optimal (Lambertian) light trapping, which can be achieved by inserting proper photonic structures in the solar cell architecture. The effects of extrinsic (bulk and surface) recombinations on the conversion efficiency are discussed. We also show how the main conclusions and trends can be described using relatively simple analytic models. Prospects for overcoming the 29% limit by means of silicon/perovskite tandems are briefly discussed.