In this thesis, I develop a novel time-domain approach for nonlinear scattering theory (NLST), a previously frequency domain method for estimating the nonlinear generation from a nanostructure. Due to a gap in literature, I then perform a full comparison of this novel time domain approach to the existing one in the frequency domain. Using the example scenario of third harmonic generation from various media in 1D and 3D, I compare - quantitatively - the NLST estimated nonlinear spectra to two types of direct nonlinear simulations: one using an experimental value for the nonlinear optical susceptibility, and, for plasmonic systems, another using a hydrodynamics model for the nonlinear plasmonic response. Through testing differing NLST approaches on these systems, I demonstrate the effectiveness of the novel time-domain NLST and assess the use cases for this method as well as the pre-existing ones. Lastly, I discuss the applicability of NLST in future works involving the inverse design process, and high-order harmonic generation.