Extreme conditions, such as ultra-low temperatures, high pressures, and strong magnetic fields, are critical to producing and studying exotic states of matter. To measure physical properties under extreme conditions, the advanced sensing schemes are required. As a promising quantum sensor, the diamond nitrogen-vacancy (NV) center can detect magnetic field, electronic field, pressure, and temperature with high sensitivity. Considering its nanoscale spatial resolution and ultra-wide working range, the diamond quantum sensing can play an important role in frontier studies involving extreme conditions. This paper reviews the spin and optical properties of diamond NV center under extreme conditions, including low temperature, high temperature, zero field, strong magnetic fields, and high pressures. The opportunities and challenges of diamond quantum sensing under extreme conditions are discussed. The basic knowledge of spin-based quantum sensing and its applications under extreme conditions are also covered.