Composite materials for strengthening existing structural elements are a valid alternative to the traditional techniques. FRPs (Fiber-Reinforced Polymer) and FRCMs (Fiber-Reinforced Cementitous Matrix) represent an effective solution to strengthen existing concrete and masonry structures. FRCMs systems are considered a suitable alternative to FRPs when drawbacks associated with the use of organic binders could compromise the strengthening intervention. Both FRPs and FRCMs are EBR (Externally bonded reinforcement), so the effectiveness of composite reinforced materials is influenced by the bond behaviour at different interfaces. The bond depends on many parameters, e.g. bond length, mechanical properties of substrate and reinforcement, environmental conditions, etc. Differently from FRPs, for which the bond between fiber and resin is of chemical nature thanks to the polymerization process of organic matrix, the interaction between inorganic matrix and fibers is mostly of mechanical type. In fact, inorganic binders can hardly impregnate all fiber filaments, which leads often to a debonding phenomenon at the matrix-fabric interface. Therefore, there is the need to calibrate new theoretical models as a function of new parameters. At this scope, a deep analysis of the state of the art on bond tests on masonry and concrete elements reinforced with different FRCM systems were conducted. A large database was created. For each sample, the mechanical and geometrical characteristics of substrate, mortar, dry fiber and FRCM were reported. The experimental results, instead, were collected in terms of peak load, conventional limit stress, slip and failure mode. With the aim to identify which parameter affect the bond between substrate and FRCM, the data was divided in concrete and masonry elements and then subdivided according to failure mode (debonding, slipping and fiber rupture at the free end). For each group, the dependence between conventional limit stress and bond strength and the collected parameters was searched. Then, regression analyses were carried out to calibrate reliable formulation predicting the maxim strain and the bond strength according to the previously identified parameters.