Inspired by its ubiquity in nature, self-organization of synthetic chemical systems is currently quickly developing into a powerful strategy for the design of new functional materials. As self-organization requires the system to exist far from thermodynamic equilibrium, chemists have begun to go beyond classical equilibrium self-assembly often applied in the bottom-up supramolecular synthesis and to learn about the surprising and unpredicted emergent properties of chemical systems that are characterized by a higher level of complexity and extended reactivity networks. The present review focuses on self-organization in reaction-diffusion systems. Selected examples show how the emergence of complex morphogenesis is feasible in synthetic systems leading to hierarchically and nano-structured matter. Starting from well-investigated oscillating reactions, recent developments extend diffusion-limited reactivity to supramolecular systems. The concept of dynamic instability is introduced and illustrated as an additional tool for the design of smart materials and actuators, with emphasis on the realization of motion even at the macroscopic scale. The formation of spatio-temporal patterns along diffusive chemical gradients is exploited as the main channel to realize symmetry breaking and therefore anisotropic and directional mechanical transformations. Finally, the interaction between external perturbations and chemical gradients is explored to give mechanistic insights in the design of materials responsive to external stimuli.