The primary purpose of a census is to provide accurate estimates of a country's population. These underpin a myriad of key planning decisions in between consecutive censuses at both the local and national level. In addition, reliable census data is needed at an international level. For example, the UN requires member states to take at least a census every ten years and EU member states have a statutory requirement to provide comprehensive population and housing data at regular defined periods. As such censuses have a pivotal role to play within official statistics. There are, however, different modes in which a country can conduct a census. Furthermore, despite all efforts, it is inevitable that the census cannot be perfect. Therefore, there is the need to measure the quality of the data produced in a census. The measurement of quality within a census is not an easy undertaking, mainly because there is currently no standard method of quality assessment that applies to all census methodologies. Thus this paper aims to bridge this gap, by examining quality assessment with regards to population censuses. It defines census quality, and then discusses the assessment of quality for different types of censuses.