Multiple imputation for non-response replaces each missing value by two or more plausible values. The values can be chosen to represent both uncertainty about the reasons for non-response and uncertainty about which values to impute assuming the reasons for non-response are known. This paper provides an overview of methods for creating and analysing multiply-imputed data sets, and illustrates the dramatic improvements possible when using multiple rather than single imputation. A major application of multiple imputation to public-use files from the 1970 census is discussed, and several exploratory studies related to health care that have used multiple imputation are described.