The detection of current is critical within the context of industrial and power systems. Precise quantification of current is essential to ensure normal equipment functionality, enhance work productivity, and maintain the safety and integrity of power systems. This paper provides an overview of conventional current sensors and highlights the performance differences in current detection. The discussion encompasses current transformers, Rogowski coils, fiber optic current sensors, flux gates, and Hall current sensors. In light of the increasing complexity of current sensing requirements, conventional current sensors face challenges in meeting these demands. Thus, this study presents a comprehensive review of the development and fundamental principles of magnetoresistive sensors. This incorporates anisotropic magnetoresistive sensors, giant magnetoresistive sensors, and tunnel magnetoresistive sensors. Additionally, this paper examines the application of magnetoresistive sensors in current detection. Finally, the paper discusses the challenges and issues faced by magnetoresistive sensors in current detection, alongside the potential for future development trends.