In radiation-based medical imaging research, computational modeling methods are used to design and validate imaging systems and post-processing algorithms. Monte Carlo methods are widely used for the computational modeling as they can model the systems accurately and intuitively by sampling interactions between particles and imaging subject with known probability distributions. This article reviews the physics behind Monte Carlo methods, their applications in medical imaging, and available MC codes for medical imaging research. Additionally, potential research areas related to Monte Carlo for medical imaging are discussed.