Non-market, not-for-profit, or social housing takes many forms and has a wide range of potential economic and social consequences, which have been much debated and continue to arouse controversy. While such housing may arise as a response to market failures, it more usually arises as a political response to inequality arising from some combination of housing shortage, insecurity and high costs. Many economists have argued that while there is much evidence of different forms of market failure, these do not in themselves justify the provision of non-market housing either directly by the state or indirectly by subsidising other providers. The first objective of this chapter is to understand the economic basis for social housing and to address the validity or otherwise of conventional economic critiques of it. It will further explore newer thinking, such as new institutional economics. The second objective is to consider the arguments for and against different forms of subsidy, in particular, the debate among demand-side subsidies, cash transfers and specific dwelling or price (supply-side) subsidies. This critique will be used to assess how economic analysis can inform the design of an efficient and fair demand-side allowance, either instead of or in addition to subsidised social housing.