Magnetic field sensing plays an important role in many fields of scientific research and engineering applications. Benefiting from the advantages of optical fibers, the optical fiber-based magnetic field sensors demonstrate characteristics of light weight, small size, remote controllability, reliable security, and wide dynamic ranges. This paper provides an overview of the basic principles, development, and applications of optical fiber magnetic field sensors. The sensing mechanisms of fiber grating, interferometric and evanescent field fiber are discussed in detail. Magnetic fluid materials, magneto-strictive materials, and magneto-optical materials used in optical fiber sensing systems are also introduced. The applications of optical fiber magnetic field sensors as current sensors, geomagnetic monitoring, and quasi-distributed magnetic sensors are presented. In addition, challenges and future development directions are analyzed.