The excitation of surface plasmons in metallic nanoparticles induces optical properties hardly achievable in other optical materials, yielding a wide range of applications in many fields. This review presents an overview of surface plasmons in metallic nanoparticles. The concept of surface plasmons in nanoparticles is qualitatively described using a comparison with simple linear oscillators. The mathematical models to carry on calculations on surface plasmons are presented as well as the most common approximations. The different parameters governing the features of surface plasmons and their effect on the optical properties of the materials are reviewed. Finally, applications of surface plasmons in different fields as biomedicine, energy, environment protection and information technology are revised.