Android apps are daily installed by billions of users worldwide, who grant access to an extensive set of sensitive personal data. Different techniques have been developed over the years to understand how apps protect or harm their users’ privacy. However, these results have been produced in different research domains and addressing privacy from different perspectives, resulting in a growing but scattered body of knowledge. To bridge this gap, we have carried out a systematic mapping study to provide practitioners and researchers with an overview of the state-of-the-art technique, published between 2016 and 2020, to assess privacy in Android apps. In this paper, we highlight the most relevant findings, identify and analyse the most pressing gaps, and discuss the promising research directions.