‘Smart’ structural health monitoring of composite materials with optical fiber sensors is becoming more and more important, especially in the aviation industry. This paper presents an overview of hybrid fiber-optic sensing systems based on scattering techniques, fiber Bragg gratings, interferometric techniques, and polarimetric methods in structural health monitoring. The main purpose of this manuscript is to analyze the possibilities of using hybrid sensors based on fiber optics to monitor composite structures, with a particular emphasis on aircraft structures. Since it is difficult to indicate the most comprehensive approach due to different parameters of the described sensors, the review contains a detailed description of available solutions. We hope that this work will allow for a better and faster selection of the right solution for the problem at hand.