Despite their broad clinical use, conventional drug delivery technologies are still limited by inadequate bioavailability, non-specific biodistribution, and uncontrolled drug release, which compromise therapeutic efficacy and safety. With their customizable molecular architecture, physicochemical adaptability, and multifunctional, stimuli-responsive design, next-generation polymeric materials overcome these constraints and allow for precise, site-specific, and regulated therapeutic action. In addition to stimuli-responsive platforms and structurally diverse nanocarriers such as nanoparticles, micelles, dendrimers, polymerases, and nanogels, this review critically examines the molecular and physicochemical design principles, nanoengineering and fabrication strategies, such as self-assembly, microfluidics, and emerging 3D/4D printing. Moreover, the passive, active, and organelle-level targeting mechanisms that govern these systems. In addition to clinical translation challenges, existing research gaps, and emerging directions like sustainable polymer chemistry, AI-driven design, adaptive 4D-printed systems, and personalized therapeutics, their disease-specific applications in cancer, neurological, cardiovascular, and infectious diseases, chronic wound healing, and regenerative medicine are critically evaluated. When taken as a whole, next-generation polymeric materials provide a flexible, clinically translatable platform for accurate, effective, and safe therapeutic intervention. However, they also highlight the crucial issues that need to be addressed in order to expedite clinical translation.