We present theoretical and computational findings regarding second harmonic generation within plasmonic and all-dielectric metamaterials. An in-depth analysis of the surface and bulk contributions to the second harmonic signal in centrosymmetric metaatoms is undertaken, whereby it is found that a common assumption of neglecting the bulk portion of dielectric structures is unjustified. An all-dielectric metamaterial unit cell is also presented. The power radiated by the electromagnetic dipoles are calculated alongside the electric quadrupole for both the linear and nonlinear regime for a LiTaO3 meta-atom. A nonlinear resonance that is engendered by the linear toroidal dipole is also shown to be toroidal in nature. A structure consisting of gold split ring resonators embedded in a dielectric is designed to have a strong nonlinear toroidal dipole. The optical spectra of the metamaterial array are simulated, with the powers radiated by the electric, magnetic and toroidal dipoles being compared at the second harmonic, whereby the toroidal dipole dominates. In a separate investigation, we analyse computationally and experimentally optical meta-atoms that generate two distinct resonances in frequency-space for applications in laser protection. Different polarisation-dependent designs are incorporated to produce a polarisation-independent meta-atom. The optical response of this cross-shaped structure is calculated and compared with a fabricated structure. The simulation and fabrication process is analysed in detail. Additional to this investigation, a notch filter is designed through using DiffractMOD's MOST optimizer and subsequently manufactured in the London Centre for Nanotechnology. The transmission coefficients are again measured. Furthermore, a Bragg/metamaterial composite is briefly introduced and analysed. This new composite is intended to improve performance on the previous transmission notch filter by having the metamaterial effectively act as a substitute for a number of layers of the Bragg filter.