Arch-shaped members are widely used for construction of tunnels, bridges, silos and shells. These members are not typically provided with transverse reinforcement and may thus have a brittle behaviour at failure. When subjected to bending or shear, traditional design methods used for straight members are not applicable due to deviation forces developing at the curved chords carrying compression and tension, which is not always accounted in design codes. In this paper, two experimental series on arch-shaped members tested by the authors are reviewed. The first series comprises six arch-shaped members subjected to pure bending. In this case, premature spalling failures were observed due to the deviation forces of the tensile reinforcement. The observed strength to spalling is seen to be closely related to the deformation of the tensile reinforcement, indicating the interaction between bond and deviation forces. A consistent approach for their design combining these two effects is proposed and validated The second series comprises nine specimens subjected to bending and shear. The curvature of the specimens is shown to have a positive or detrimental effect on the shear strength depending on the curvature of the member with respect to the load (convex or concave). This effect, which may turn to be significant, is proven to be consistently accounted by the physical model of the critical shear crack theory, leading to very good predictions of the strength and failure mode of the specimens.