Interferometric Synthetic Aperture Radar (InSAR) is a powerful technology for observing the Earth surface, especially for mapping the Earth's topography and deformations. InSAR measurements are however often significantly affected by the atmosphere as the radar signals propagate through the atmosphere whose state varies both in space and in time. Great efforts have been made in recent years to better understand the properties of the atmospheric effects and to develop methods for mitigating the effects. This paper provides a systematic review of the work carried out in this area. The basic principles of atmospheric effects on repeat-pass InSAR are first introduced. The studies on the properties of the atmospheric effects, including the magnitudes of the effects determined in the various parts of the world, the spectra of the atmospheric effects, the isotropic properties and the statistical distributions of the effects, are then discussed. The various methods developed for mitigating the atmospheric effects are then reviewed, including the methods that are based on PSInSAR processing, the methods that are based on interferogram modeling, and those that are based on external data such as GPS observations, ground meteorological data, and satellite data including those from the MODIS and MERIS. Two examples that use MODIS and MERIS data respectively to calibrate atmospheric effects on InSAR are also given.