The variety of possibilities for customizing web browser, combined with the capacity of a remote server to query information without requesting any permission, has created a new kind of privacy issue called browser fingerprinting. Previous studies demonstrated the effectiveness of fingerprinting to uniquely identify browsers running on laptops and desktops. Meanwhile, the majority of browsing activities have switched from laptops to mobile devices. Yet, there is currently a lack of systematic analysis of browser fingerprinting on mobile devices. In this paper, we describe browser fingerprinting technologies and summarize previous observations on laptops. Then, we present preliminary observations on mobile devices, highlighting differences with previous results, and challenges for future work.