The compound parabolic concentrator (CPC) is not a specific collector, but a family of collectors based on a general design principle for maximizing the geometric concentration, C, for radiation within a given acceptance half angle ±θc. This maximum limit exceeds by a factor of 2 to 4 that attainable by systems using focusing optics. The wide acceptance angles permitted using these techniques have several unique advantages for solar concentrators including the elimination of the diurnal tracking requirement at intermediate concentrations (up to ~10x), collection of circumsolar and some diffuse radiation and relaxed tolerances. Because of these advantages, CPC type concentrators have applications in solar energy wherever concentration is desired, e.g., for a wide variety of both thermal and photovoltaic uses. The basic principles of nonimaging optical design are reviewed. Selected configurations for both non-evacuated and evacuated thermal collector applications are discussed with particular emphasis on the most recent advances. The use of CPC type elements as secondary concentrators is illustrated in the context of higher concentration photovoltaic applications.