Gold nanostars (AuNSs) are nanoparticles with intricate three-dimensional structures and shape-dependent optoelectronic properties. For example, AuNSs uniquely display three distinct surface curvatures, i.e. neutral, positive, and negative, which provide different environments to adsorbed ligands. Hence, these curvatures are used to introduce different surface chemistries in nanoparticles. This review summarizes and discusses the role of surface curvature in AuNS properties and its impact on biomedical and chemical applications, including surface-enhanced Raman spectroscopy, contrast agent performance, and catalysis. We examine the main synthetic approaches to generate AuNSs, control their morphology, and discuss their benefits and drawbacks. We also describe the optical characteristics of AuNSs and discuss how these depend on nanoparticle morphology. Finally, we analyze how AuNS surface curvature endows them with properties distinctly different from those of other nanoparticles, such as strong electromagnetic fields at the tips and increased hydrophilic environments at the indentations, together making AuNSs uniquely useful for biosensing, imaging, and local chemical manipulation.