Current sensors play a vital role in power systems, industrial production, smart devices and other fields, which can provide critical current information in the systems for the safety and efficiency managements. The development of magneto-resistive effect technology in recent years expedites the research process of the current sensors in industrial-level applications. In the review, starting with the development status of the current sensors, the physical mechanisms of the relevant magneto-resistive effects and their early applications as the current sensors are introduced. Several design methods of the magnetic sensors, as well as their merits and shortcomings, are summarized. The performance parameters of the magnetic sensors based on AMR, GMR, TMR and Hall effects are reviewed, including the front-end amplification circuits and conditioning circuits. The industrial applications of the current sensors in the fields of automobiles and photovoltaic inverters are enumerated. The criterions for the current sensors to be used in different scenarios are discussed. In the future, it is imperative to continue the research and development of novel current sensors in order to satisfy the increasingly stringent demands of the industrial developments, in terms of the performance, cost and reliability of the current sensors.