In recent years, mobile devices (e.g., smartphones and tablets) have met an increasing commercial success and have become a fundamental element of the everyday life for billions of people all around the world. Mobile devices are used not only for traditional communication activities (e.g., voice calls and messages) but also for more advanced tasks made possible by an enormous amount of multi-purpose applications (e.g., finance, gaming, and shopping). As a result, those devices generate a significant network traffic (a consistent part of the overall Internet traffic). For this reason, the research community has been investigating security and privacy issues that are related to the network traffic generated by mobile devices, which could be analyzed to obtain information useful for a variety of goals (ranging from device security and network optimization, to fine-grained user profiling). In this paper, we review the works that contributed to the state of the art of network traffic analysis targeting mobile devices. In particular, we present a systematic classification of the works in the literature according to three criteria: (i) the goal of the analysis; (ii) the point where the network traffic is captured; and (iii) the targeted mobile platforms. In this survey, we consider points of capturing such as Wi-Fi Access Points, software simulation, and inside real mobile devices or emulators. For the surveyed works, we review and compare analysis techniques, validation methods, and achieved results. We also discuss possible countermeasures, challenges and possible directions for future research on mobile traffic analysis and other emerging domains (e.g., Internet of Things). We believe our survey will be a reference work for researchers and practitioners in this research field.