Fiber Bragg gratings (FBGs) are point optical fiber sensors that allow the monitoring of a diversity of environmental parameters, e.g., temperature or strain. Several research groups have studied radiation effects on the grating response, as they are implemented in harsh environments: high energy physics, space, and nuclear facilities. We report here the advances made to date in studies regarding the vulnerability and hardening of this sensor under radiation. First, we introduce its principle of operation. Second, the different grating inscription techniques are briefly illustrated as well as the differences among the various types. Then, we focus on the radiation effects induced on different FBGs. Radiation induces a shift in their Bragg wavelengths, which is a property serving to measure environmental parameters. This radiation-induced Bragg wavelength shift (RI-BWS) leads to a measurement error, whose amplitude and kinetics depend on many parameters: inscription conditions, fiber type, pre- or post-treatments, and irradiation conditions (nature, dose, dose rate, and temperature). Indeed, the radiation hardness of an FBG is not directly related to that of the fiber where it has been photo-inscribed by a laser. We review the influence of all these parameters and discuss how it is possible to manufacture FBGs with limited RI-BWS, opening the way to their implementation in radiation-rich environments.