Population censuses provide a wide range of detailed information, but are expensive and infrequent. Some more frequent information can be obtained using administrative data sources, which can also be combined with some directly collected information. This combination of sources requires new approaches to produce objective census estimates. We apply methods to deal with undercoverage and overcoverage in administrative data in different contexts, and to examine the quality of population estimates based on administrative data sources, based on the application of dual and multiple system estimation. We also apply novel design methods to the traditional census operation in the UK.