Static (or stationary) concentration opens up a promising path towards a reduction of the cost of photovoltaic electricity. This paper presents a review of the state-of-the art of static concentrators, including the theoretical basis of design and analysis, as well as some experimental prototypes. The limits of concentration and the conditions under which they may be reached are described. The limit is about 8 for a concentrator collecting 100% of direct radiation and about 45% of diffuse radiation. The two available design methods of 2-D static concentrators are briefly outlined.