This thesis covers three different topics. The first part is a pedagogical review of the basic principles and recent advances in nonlinear optics. It was originally written as a chapter for the proceedings of the “International School of Physics (Enrico Fermi)” summer school on Photonics held in June, 2014. It is included to provide some background information about nonlinear optical processes in general, and is particularly relevant for the third part of this thesis which is based on the second-order nonlinear optical process of spontaneous parametric downconversion. The second part is based on original research, and deals with superradiance in plasmonic nanostructures. The process of superradiance, as introduced by Dicke in 1954, entails the shortening of the spontaneous emission lifetime of a collection of N quantum emitters as a consequence of the development of a macroscopic dipole moment. Specifically, the lifetime is shortened by a factor of 1/N, and the linewidth is broadened by a factor of N. Such a linewidth dependence has been previously observed in systems of several plasmonic ‘emitters’. However, a clear physical insight into this phenomenon and how it relates to Dicke superradiance has not been shown yet. In this part, we demonstrate by experiment, simulation, and a simple analytical model that Dicke’s superradiance can indeed be observed in a planar array of plasmonic nanoantennas, with a linewidth that scales linearly with the number of nanoantennas within a square wavelength. The third part is also based on original research, and is based on the scal- ing laws of spontaneous parametric downconversion (SPDC) for a type-I phase- matching configuration. The variation of bi-photon generation rate, heralding efficiency and radiance with parameters such as crystal length, pump focussing and collection waist sizes are examined for collinear and non-collinear emission. The results can be used to maximize the brightness of the SPDC source or increase the heralding efficiency depending on the application.