During last decades, Magnetic Resonance (MR)--compatible sensors based on different techniques have been developed due to growing demand for application in medicine. There are several technological solutions to design MR-compatible sensors, among them, the one based on optical fibers presents several attractive features. The high elasticity and small size allow designing miniaturized fiber optic sensors (FOS) with metrological characteristics (e.g., accuracy, sensitivity, zero drift, and frequency response) adequate for most common medical applications; the immunity from electromagnetic interference and the absence of electrical connection to the patient make FOS suitable to be used in high electromagnetic field and intrinsically safer than conventional technologies. These two features further heightened the potential role of FOS in medicine making them especially attractive for application in MRI. This paper provides an overview of MR-compatible FOS, focusing on the sensors employed for measuring physical parameters in medicine (i.e., temperature, force, torque, strain, and position). The working principles of the most promising FOS are reviewed in terms of their relevant advantages and disadvantages, together with their applications in medicine.