The paper reviews attempts to provide insurance against risks afflicting the poorest. It presents empirical evidence on the impact of different types of microinsurance, and recommends the idea of 'quasi-insurance' -- the provision of insurance functions through a non-insurance route -- where institutional or regulatory constraints prevent insurance proper from being offered. The paper argues that microinsurance so far has been somewhat supply-driven rather than driven by effective demand, especially from the poorest, and thus the insurance products which would benefit the poorest are still at a limited stage of development. Institutional innovations and new insurance products therefore deserve promotion. 1. Introduction -- 2. Basic principles: organisation, pricing and incentives -- 3. What does microfinance achieve? Some preliminary findings -- 4. 'Quasi-insurance': Financial substitutes for microinsurance proper -- 5. Conclusions for policy and institutional design -- Appendix 1. Weather insurance schemes: more details -- Appendix 2. 'Smart-subsidies' for poverty-reducing institutional changes.