The main problems facing annuity providers relate to adverse selection and mortality risk, the risk associated with mortality improvements, and to interest rate, reinvestment and inflation risk. Annuity providers hedge these risks, wherever possible, by holding suitable matching assets against their annuity liabilities: for example, riskless (government) fixed-income bonds are used to provide the payments on level annuities, and index-linked bonds are needed if index-linked annuities are to be serviced effectively. However, in the absence of suitable matching assets, providers are unable to hedge the risks associated with mortality effectively and compensate for this by imposing substantial cost loadings. They also face reinvestment risk if available assets are of insufficient duration. Annuitants face interest rate risk prior to purchase and, since most of them prefer the higher initial income from a level annuity compared with an indexed annuity, inflation risk after purchase. Some solutions to these problems are considered, including a planned programme of phased annuity purchases to hedge interest rate risk, limited price index bonds to partially hedge inflation risk, and survivor (or indexed life) bonds, with coupons declining in direct proportion to the realized mortality of a selected group of annuitants, to hedge mortality risk. Finally, we examine the advantages and disadvantages of different institutional forms for the annuity market, ranging from monopoly provision through limited licensed provision to a fully competitive provision.