Some 175 years ago Michael Faraday discovered magnetic circular birefringence, now commonly known as the Faraday effect. Sensing the magnetic field through the influence that the field has on light within the fiber optic sensor offers several advantages, one of them fundamental. These advantages find application in the measurement of electric current at high voltages by measuring the induced magnetic field, thus warranting application for this kind of fiber optic sensor (FOS) in future smart grids. Difficulties in designing and manufacturing high-performance FOSs were greatly alleviated by developments in optical telecommunication technology, thus giving new impetus to magnetometry based on the Faraday effect. Some of the major problems in the processing of optical signals and temperature dependence have been resolved, yet much effort is still needed to implement all solutions into a single commercial device. Artificial structures with giant Faraday rotation, reported in the literature in the 21st century, will further improve the performance of FOSs based on the Faraday effect. This paper will consider obstacles and limits imposed by the available technology and review solutions proposed so far for fiber optic sensors based on the Faraday effect.