Many very sensitive analytical methods utilising specific properties of plasmonic metal nanoparticles have been developed. Some of these techniques are so sensitive that observation of the reliable signal even from a single molecule of the analyte is possible. In this review article we present the most important analytical techniques based on the plasmonic properties of selected metal nanoparticles and the basic theoretical background of these analytical techniques, including the mechanism of the interaction of the electromagnetic radiation with the plasmonic nanoparticles. The analytical techniques presented in this article include methods based on the change of the optical properties of plasmonic nanoparticles caused by analyte-induced aggregation, etching or the change of the growth of plasmonic nanoparticles, and techniques utilising increased efficiency of some optical processes in the proximity of the plasmonic nanoparticles, e.g. surface-enhanced Raman scattering (SERS), surface enhanced infra-red absorption (SEIRA), and metal enhanced fluorescence (MEF). Recently, an observed increase in the number of applications of techniques utilising surface plasmon resonance for the analysis of various industrial, biological, medical, and environmental samples allows us to predict a large increase of the significance of these techniques in the near future.