Proteins, genetic material, and membranes are fundamental to all known organisms, yet these components alone do not constitute life. Life emerges from the dynamic processes of self-organization, assembly, and active motion, suggesting the existence of similar artificial systems. Against this backdrop, our Perspective explores a variety of chemical phenomena illustrating how nonequilibrium self-organization and micromotors contribute to life-like behavior and functionalities. After explaining key terms, we discuss specific examples including enzymatic motion, diffusiophoretic and bubble-driven self-propulsion, pattern-forming reaction-diffusion systems, self-assembling inorganic aggregates, and hierarchically emergent phenomena. We also provide a roadmap for combining self-organization and active motion and discuss possible outcomes through biological analogs. We suggest that this research direction, deeply rooted in physical chemistry, offers opportunities for further development with broad impacts on related sciences and technologies.