Shape-morphing bilayer composites perform reversible deformation when a stimulus is applied. These material systems have attracted attention due to the promising applications in sensors, actuators, self-folding structures, and soft robotics. This research investigates, by modelling and experimental approaches, thermally triggered shape-morphing behaviour of reduced graphene oxide (rGO) filled chitosan-methacrylamide/polydimethylsiloxane (rGO-chitosan-MA/PDMS) and rGO-chitosan-norbornene/PDMS (rGO-chitosan-NB/PDMS) bilayer composites. In the experimental study, the mechanical and thermal properties of the bilayer constituent materials are characterised. Moreover, the photothermal shape-morphing behaviour of the bilayer composites is characterised. In the modelling study, a non-linear multiphysics finite element analysis (FEA) model is created to simulate shape-morphing of the bilayer systems. FEA simulations are compared with analytical solutions of deflection, stress, and strain to validate some of the assumptions and simplification of the FEA model. The degree of error of the FEA model is obtained comparing FEA simulations with measured shape-morphing data. Furthermore, geometrical optimisation of the bilayer composites is performed, shape-morphing of a bilayer with tapered thickness on the rGO-chitosan-NB layer is simulated, the potential of the rGO-chitosan-MA/PDMS bilayer to be used in actuation systems is investigated, and self-folding driven by bilayer hinges is studied to provide design guidelines. Finally, a novel crawling soft-robot is designed based on tapered thickness bilayer systems and hinge-like folding. The crawling robot is simulated and physically tested; it performs remote controlled unidirectional crawling due to asymmetric shape-morphing and imbalance of friction forces between the contact areas of the robot with a rough surface.