With the mass-manufacture and resulting low cost of silicon photovoltaics driven by Western government subsidy schemes and large-scale manufacturing, concentrated solar power for electricity generation is now at a turning point. The present cost of mirrors, lenses, support structure and plant for concentrated solar thermal power, and of the highefficiency multi-junction cells, concentrating optics and two-axis tracking systems for concentrated photovoltaic power, has made operational concentrated solar power plants uncompetitive in most scenarios. This is changing the shape of optics as well as the materials from which they are constructed and the size of the components used. We aim to highlight the current research that is being carried out to reduce the cost of concentrated solar power and concentrate on the long-term potential for cost reduction of both concentrated solar power technologies. This review concentrates first on optical and thermodynamic fundamentals, and the technology choices imposed by real world materials. We then review the broad categories of optical concentrators. Developments in solar thermal power generation and heat and thermochemical storage are discussed before briefly describing recent research on thermoelectric generation. Recent trends in concentrated photovoltaics are summarised, and we conclude by considering the present situation for concentrated solar power in the context of mass-market silicon photovoltaics.