Microinsurance - or the insurance for the poor - has been considered as "the next revolution" in addressing risks and vulnerability in low-income countries. In particular, huge investments have been made in the last decade by several development agencies (among which USAID and the Gates foundation) in this revolutionary tool that promised to break the circle of poverty and offer a reliable protection to the poor. The focus of this review is on low-income countries, where adverse shocks are frequent, and risk-pooling mechanisms and self-insurance strategies are imperfect. As poor individuals also display a relatively high level of risk aversion, the demand for microinsurance products is thus expected to be high. However, the evidence is disappointing: subscription to the widely subsidized insurance schemes is low, rarely above 30%. Renewal rates are also exceptionally modest. The present paper addresses this puzzle first from a theoretical point of view and then reviews the empirical evidence on the factors influencing demand for insurance.