This dissertation contains analytical and numerical studies of nonlinear surface-plasmon polaritons (SPPs). In our studies, we consider SPP propagation at the interface between a noble metal with a cubic optical nonlinearity and an optically linear dielectric. We first consider a sum-frequency generation process during the nonlinear interaction, where a nonlinear polarization with tripled frequency is generated from the incident fundamental SPP. Using the non-depletion approximation, the solution of the nonlinear wave equation shows a third harmonic generation process from the incident SPP wave. The solution is bound in the dielectric while freely propagating in the metal. For realistic noble metals with absorption, we use silver for its transparency window around the plasma frequency. In this window, absorption losses are reduced and the resultant signal has a good transmittance within the metal. The energy conversion efficiency from the incident SPP wave to the THG signal is about 0.1% for excitation using a standard continuous wave laser with visible light intensity I = 103W/cm2. Once generated, the propagation angle of the signal is fully determined by the optical properties of the dielectric and the metal layers. We next consider a nonlinear polarization with the same frequency as the incident light. In this process the third order nonlinearity of the metal is described by a nonlinear optical refractive-index. With the slowly varying amplitude approximation, the nonlinear wave equation takes the form of a nonlinear temporal Schr¨odinger (NLS) equation. The solution to the NLS equation for the nonlinear SPP is a temporal dark soliton (TDS). In addition to analytical studies, computational methods are also used. With no metal loss, the numerical solution shows stable propagation of a TDS, when the initial pulse has a tanh envelope satisfying the threshold peak amplitude. For an arbitrary input pulse, instabilities such as background-oscillations and multi-peak breakups occur. With metal loss, the input optical pulse decays while maintaining a single pulse shape when the initial amplitude satisfies the same tanh envelope condition as in the lossless case. For an arbitrary pulse, background-oscillations or pulse-breakups occur after a short time of propagation.