This article provides the comprehensive analysis of the core mechanisms underlying anonymous browsers, with a focus on the modern Tor browser. It explores the principles of onion routing, detailing the multi-layered encryption process that ensures anonymity and prevents third-party tracking. The study examines how encryption keys are exchanged between nodes and how the network dynamically adjusts to maintain security and performance. Additionally, the work delves into potential vulnerabilities within the Tor network, including risks associated with exit nodes, traffic correlation attacks, and fingerprinting techniques that could compromise user anonymity.