Information on the origin of pollution is an essential element of air quality management that helps identifying measures to control air pollution. In this document, we review the most widely used source-apportionment (SA) methods for air quality management. The focus is on particulate matter but examples are provided for NO2 as well. Using simple theoretical examples, we explain the differences between these methods and the circumstances where they give different results and thus possibly different conclusions for air quality management. These differences are a consequence of the assumptions that underpin each methodology and determine/limit their range of applicability. We show that ignoring these underlying assumptions is a risk for efficient/successful air quality management when the methods are used outside their scope or range of applicability.