The intermediate band (IB) solar cell has been proposed to increase the current of solar cells while at the same time preserving the output voltage in order to produce an efficiency that ideally is above the limit established by Shockley and Queisser in 1961. The concept is described and the present realizations and acquired understanding are explained. Quantum dots are used to make the cells but the efficiencies that have been achieved so far are not yet satisfactory. Possible ways to overcome the issues involved are depicted. Alternatively, and against early predictions, IB alloys have been prepared and cells that undoubtedly display the IB behavior have been fabricated, although their efficiency is still low. Full development of this concept is not trivial but it is expected that once the development of IB solar cells is fully mastered, IB solar cells should be able to operate in tandem in concentrators with very high efficiencies or as thin cells at low cost with efficiencies above the present ones.