Porous organic polymers have received considerable attention in recent years because of their applicability as biomaterials. In particular, their hierarchical pore structures, variable morphologies, and tunable biological properties make them suitable as drug-delivery systems. In this review, the synthetic and post forming/control methods including templated methods, template-free methods, mechanical methods, electrospun methods, and 3D printing methods for controlling the hierarchical structures and morphologies of porous organic polymers are discussed, and the different methods affecting their specific surface areas, hierarchical structures, and unique morphologies are highlighted in detail. In addition, we discuss their applications in drug encapsulation and the development of stimuli (pH, heat, light, and dual-stimuli)-responsive materials, focusing on their use for targeted drug release and as therapeutic agents. Finally, we present an outlook concerning the research directions and applications of porous polymer-based drug delivery systems.