The history of Compton cameras began with the detection of radiation sources originally for applications in astronomy. A Compton camera is a promising γ-ray detector that operates in the wide energy range of a few tens of keV to MeV. The γ-ray detection method of a Compton camera is based on Compton scattering kinematics, which is used to determine the direction and energy of the γ-rays without using a mechanical collimator. Although the Compton camera was originally designed for astrophysical applications, it was later applied in medical imaging as well. Moreover, its application in environmental radiation measurements is also under study. Although a few review papers regarding Compton cameras have been published, they either focus very specifically on the detectors used in such cameras or the particular applications of Compton cameras. Thus, the aim of this paper is to review the features and types of Compton cameras and introduce their applications, associated imaging algorithms, improvement scopes, and their future aspects.