One of the new materials that have recently attracted wide attention of researchers are magnetoelectric (ME) composites. Great interest in these materials is due to their properties associated with the transformation of electric polarization/magnetization under the influence of external magnetic/electric fields and the possibility of their use to create new devices. In the proposed review, ME magnetic field sensors based on the widely used structures Terfenol—PZT/PMN-PT, Metglas—PZT/PMN-PT, and Metglas—Lithium niobate, among others, are considered as the first applications of the ME effect in technology. Estimates of the parameters of ME sensors are given, and comparative characteristics of magnetic field sensors are presented. Taking into account the high sensitivity of ME magnetic field sensors, comparable to superconducting quantum interference devices (SQUIDs), we discuss the areas of their application.