The number of mobile devices, such as smartphones and smartwatches, is relentlessly increasing to almost 6.8 billion by 2022, and along with it, the amount of personal and sensitive data captured by them. This survey overviews the state of the art of what personal and sensitive user attributes can be extracted from mobile device sensors, emphasising critical aspects such as demographics, health and body features, activity and behaviour recognition, etc. In addition, we review popular metrics in the literature to quantify the degree of privacy, and discuss powerful privacy methods to protect the sensitive data while preserving data utility for analysis. Finally, open research questions are presented for further advancements in the field.