Extensive literature and publications on intermediate band solar cells (IBSCs) are reviewed. A detailed discussion is given on the thermodynamics of solar energy conversion in IBSCs, the device physics, and the carrier dynamics processes with a particular emphasis on the two-step inter-subband absorption/recombination processes that are of paramount importance in a successful implementation high-efficiency IBSC. The experimental solar cell performance is further discussed, which has been recently demonstrated by using highly mismatched alloys and high-density quantum dot arrays and superlattice. IBSCs having widely different structures, materials, and spectral responses are also covered, as is the optimization of device parameters to achieve maximum performance.