Smartphones and Internet have become prevalent in our society with various applications in businesses, education, healthcare, gaming, and research. One of the major issues with the Internet today is its lack of security since an eavesdropper can potentially intercept the communication. This has contributed towards an increased number of cyber-crime incidents, resulting in an increase in users' consciousness about the security and privacy of their communication. One example is the shift towards using private browsers such as Tor. Tor is a well-recognized and widely used privacy browser based on The Onion Router network that provisions anonymity over the insecure Internet. This functionality of Tor has been a major hurdle in cybercrime investigations due to the complex nature of its anonymity. This paper investigates artifacts from the Tor privacy browser on the latest Windows 10 and Android 10 devices to determine potential areas where evidence can be found. We examine the registry, storage, and memory of Windows 10 devices and the memory, storage, logs, and Zram of Android 10 devices for three possible scenarios i.e. before, during, and after use of the Tor browser. Our results do not support the claims made by the Tor Project regarding user privacy and anonymity. We find that it is possible to retrieve significant details about a user's browsing activities while the Tor browser is in use as well as after it is closed (on both operating systems). This paper also provides an investigative methodology for the acquisition and analysis of Tor browser artifacts from different areas of the targeted operating systems. Therefore, it can serve as a base to expand research in the forensic analysis of other privacy browsers and improve the efficiency of cybercrime investigations efficiency.