Nanosystems have shown encouraging outcomes and substantial progress in the areas of drug delivery and biomedical applications. However, the controlled and targeted delivery of drugs or genes can be limited due to their physicochemical and functional properties. In this regard, core-shell type nanoparticles are promising nanocarrier systems for controlled and targeted drug delivery applications. These functional nanoparticles are emerging as a particular class of nanosystems because of their unique advantages, including high surface area, and easy surface modification and functionalization. Such unique advantages can facilitate the use of core-shell nanoparticles for the selective mingling of two or more different functional properties in a single nanosystem to achieve the desired physicochemical properties that are essential for effective targeted drug delivery. Several types of core-shell nanoparticles, such as metallic, magnetic, silica-based, upconversion, and carbon-based core-shell nanoparticles, have been designed and developed for drug delivery applications. Keeping the scope, demand, and challenges in view, the present review explores state-of-the-art developments and advances in core-shell nanoparticle systems, the desired structure-property relationships, newly generated properties, the effects of parameter control, surface modification, and functionalization, and, last but not least, their promising applications in the fields of drug delivery, biomedical applications, and tissue engineering. This review also supports significant future research for developing multi-core and shell-based functional nanosystems to investigate nano-therapies that are needed for advanced, precise, and personalized healthcare systems.