Plasmons are collective excitations of electrons, in which the excited state involves a superposition (entanglement) of electron/hole excitations. This is in contrast with the low lying excited states of most molecules where the excitations correspond to transfer of an electron from an occupied to an unoccupied orbital. Plasmon excited states exist in all molecules and solids but they are most commonly studied in silver and gold nanoparticles, there they are responsible for the vivid colors of colloidal silver and gold. Commonly, the optical properties of plasmonic materials are described using classical electrodynamics with an empirical dielectric function, and this is extremely useful for applications in nanoscience, as it enables the description of metal structures that are hundreds of nm in size. However some spectroscopic properties, and properties that involve the transfer of charge between the metal and adsorbed molecules cannot be described this way, and it is necessary to use quantum chemistry methods instead. This sort of calculation was originally done in the 1980s, but it is only in the last 20 years that the calculations have become meaningful, as there are now metal cluster materials with well-defined structures which have been studied experimentally. In addition, calculations on metal clusters that are a few nm in size provide a very good model for the properties of 10-100nm size particles when describing such phenomena as the chemical effect in SERS, the effects of pressure on optical spectra, or plasmon-induced photocatalysis. Although many of the calculations can be done using standard electronic structure codes, there is also an important role for new theory development using the DFTB tight binding semiempirical method. Here we summarize recent developments in electronic structure studies of plasmonic clusters with up to 1000 atoms using real-time TDDFT and DFTB calculations. This has provided important mechanistic insight into many processes.