Nanotechnology is the fabrication, characterization, and potential application of various materials at the nanoscale. Over the past few decades, nanomaterials have attracted researchers from different fields because of their high surface-to-volume ratio and other unique and remarkable properties. Cobalt and cobalt oxide nanoparticles (NPs) have various biomedical applications because of their distinctive antioxidant, antimicrobial, antifungal, anticancer, larvicidal, antileishmanial, anticholinergic, wound healing, and antidiabetic properties. In addition to biomedical applications, cobalt and cobalt oxide NPs have been widely used in lithium-ion batteries, pigments and dyes, electronic thin film, capacitors, gas sensors, heterogeneous catalysis, and for environmental remediation purposes. Different chemical and physical approaches have been used to synthesize cobalt and cobalt oxide NPs; however, these methods could be associated with eco-toxicity, cost-effectiveness, high energy, and time consumption. Recently, an eco-friendly, safe, easy, and simple method has been developed by researchers, which uses biotic resources such as plant extract, microorganisms, algae, and other biomolecules such as starch and gelatin. Such biogenic cobalt and cobalt oxide NPs offer more advantages over other physicochemically synthesized methods. In this review, we have summarized the recent literature for the understanding of green synthesis of cobalt and cobalt oxide NPs, their characterization, and various biomedical applications.