In the last decades, inorganic-matrix composites have been increasingly employed as externally bonded reinforcement (EBR) for masonry and reinforced concrete (RC) members. Among them, fiber-reinforced cementitious matrix (FRCM) composites, which are comprised of high-strength open mesh textiles embedded within inorganic matrices, showed promising results for both masonry and RC strengthening. FRCMs may include different types of fiber, such as glass, carbon, basalt, polyparaphenylene benzobisoxazole (PBO), and steel, and various matrices, such as cement-based, lime-based, and geopolymers. Acceptance criteria for material qualification and design guidelines have been recently published in Europe and US. FRCMs can still be considered as relatively-new materials and the current guidelines are just a starting point. More research is needed to fully understand the behavior of structural elements strengthened with FRCM. When a single layer of fiber textile is employed, failure of FRCM-strengthened elements occurs due to debonding at the matrix-fiber interface, although different failure modes can be observed when a different number of textile layers is used. Depending on the type of application and strengthening configuration, the composite can be subjected to a multi-axial state of stress that affects the response of the strengthened member.