Electromagnetic field sensors are widely used in various areas. In recent years, great progress has been made in the optical sensing technique for electromagnetic field measurement, and varieties of corresponding sensors have been proposed. Types of magnetic field optical sensors were presented, including probes-based Faraday effect, magnetostrictive materials, and magnetic fluid. The sensing system-based Faraday effect is complex, and the sensors are mostly used in intensive magnetic field measurement. Magnetic field optical sensors based on magnetic fluid have high sensitivity compared to that based on magnetostrictive materials. Three types of electric field optical sensors are presented, including the sensor probes based on electric-optic crystal, piezoelectric materials, and electrostatic attraction. The majority of sensors are developed using the sensing scheme of combining the LiNbO3 crystal and optical fiber interferometer due to the good electro-optic properties of the crystal. The piezoelectric materials-based electric field sensors have simple structure and easy fabrication, but it is not suitable for weak electric field measurement. The sensing principle based on electrostatic attraction is less commonly-used sensing methods. This review aims at presenting the advances in optical sensing technology for electromagnetic field measurement, analyzing the principles of different types of sensors and discussing each advantage and disadvantage, as well as the future outlook on the performance improvement of sensors.