The CosmicWatch Desktop Muon Detector is a Massachusetts Institute of Technology (MIT) and Polish National Centre for Nuclear Research (NCBJ) based undergraduate-level physics project that incorporates various aspects of electronics-shop technical development. The detector was designed to be low-power and extremely portable, which opens up a wide range of physics for students to explore. This document describes the physics behind the Desktop Muon Detectors and explores possible measurements that can be made with the detectors. In particular, we explore various physical phenomena associated with the geomagnetic field, atmospheric conditions, cosmic ray shower composition, attenuation of particles in matter, radioactivity, and statistical properties of Poisson processes.