Plasmonic molecules are small assemblies of nanosized metal particles. Interactions between the particles modify their optical properties and make them attractive for multiple applications in spectroscopy and sensing. In this review, we focus on basic properties rather than on applications. Plasmonic molecules can be created using either nanofabrication methods or self-assembly techniques in solution. The interaction of plasmonic molecules with light leads to excitations that are classified using the concept of normal modes. The simplest plasmonic molecule is a dimer of particles, and its lowest energy excitation takes the form of a symmetric dipolar mode. More complex excitations take place when a larger number of particles is involved. The gaps between particles in a plasmonic molecule form hotspots in which the electromagnetic field is concentrated. Introducing molecules into these hotspots is the basis of a vast spectrum of enhanced spectroscopies, from surface-enhanced Raman scattering to surface-enhanced fluorescence and others. We show in this review how these spectroscopic methods can be used to characterize the fields around plasmonic molecules. Furthermore, the strong fields can be used to drive new phenomena, from plasmon-induced chemical reactions to strong coupling of quantum emitters with the plasmonic fields. We systematically discuss these phenomena, introducing in each case the theoretical basis as well as recent experimental realizations.