Nanomaterials have been extensively used in several applications in the past few decades related to biomedicine and healthcare. Among them, nanogels (NGs) have emerged as an important nanoplatform with the properties of both hydrogels and nanoparticles for the controlled/sustained delivery of chemo drugs, nucleic acids, or other bioactive molecules for therapeutic or diagnostic purposes. In the recent past, significant research efforts have been invested in synthesizing NGs through various synthetic methodologies such as free radical polymerization, reversible addition-fragmentation chain-transfer method (RAFT) and atom transfer radical polymerization (ATRP), as well as emulsion techniques. With further polymeric functionalizations using activated esters, thiol–ene/yne processes, imines/oximes formation, cycloadditions, nucleophilic addition reactions of isocyanates, ring-opening, and multicomponent reactions were used to obtain functionalized NGs for targeted delivery of drug and other compounds. NGs are particularly intriguing for use in the areas of diagnosis, analytics, and biomedicine due to their nanodimensionality, material characteristics, physiological stability, tunable multi-functionality, and biocompatibility. Numerous NGs with a wide range of functionalities and various external/internal stimuli-responsive modalities have been possible with novel synthetic reliable methodologies. Such continuous development of innovative, intelligent materials with novel characteristics is crucial for nanomedicine for next-generation biomedical applications. This paper reviews the synthesis and various functionalization strategies of NGs with a focus on the recent advances in different biomedical applications of these surface modified/functionalized single-/dual-/multi-responsive NGs, with various active targeting moieties, in the fields of cancer theranostics, immunotherapy, antimicrobial/antiviral, antigen presentation for the vaccine, sensing, wound healing, thrombolysis, tissue engineering, and regenerative medicine.