Apparatus for monitoring the erosion of components of industrial plants comprising at least one optical fiber sensor (7′), the optical fibers (7′) not being provided with any Bragg grid, and an analysis unit, wherein the at least one optical fiber sensor (7′) is positioned inside a wall subjected to wear by erosion in such a way as to terminate immediately under the surface of the wall itself belonging to the components (10, 10′, 20, 20′) to be monitored, and the erosion depth is measured by using the light reflected from the eroded end of the optical fiber (7′) itself.