The last decade has witnessed the development of a variety of single nanoparticle spectroscopy methods. This has facilitated unprecedented growth of knowledge and understanding of fascinating optical properties of individual metal nanoparticles. This has opened up exciting possibilities of single nanoparticles for applications in many areas including advanced photonics, biomedical imaging and sensing. The field of single nanoparticles detection and characterization is still growing. This paper reviews recent advances in single nanoparticles spectroscopy using both near-field and far-field optics. It covers spectroscopy methods for extremely small (approximately 1 nm) to relatively large nanoparticles (approximately 200 nm) and their optical properties. Different optical techniques are described. Finally, a perspective on possible practical applications of single nanoparticle spectroscopy focusing on biomedical fields is given.