"High resolution observations of Young Stellar Object (YSO) jets show them to be composed of many small-scale knots or clumps. 2-D and 3-D numerical simulations were conducted with the code AstroBEAR to study how such clumps interact and create morphologies and kinematic patterns seen in emission line observations. Two main classes of simulations were used in this study: outflows of spherical, over-dense clumps, and pulsed jets in which the pulsations create clumps within the jet. Such flows lead to the formation of bow shocks which then interact with each other as faster material overtakes slower material. We show that much of the spatial structure apparent in emission line images of jets arises from the dynamics and interactions of these bow shocks. The simulations show a variety of timedependent features, including bright knots associated with Mach stems where the shocks intersect, a 'frothy' emission structure that arises from the presence of the Non-linear Thin Shell Instability (NTSI) along the surfaces of the bow shocks, and the merging and fragmentation of clumps. Simulations with magnetic fields show how the field affects the dynamics of YSO jets and the emission they produce. This work contributes to the ultimate goal of one day being able to observationally estimate the strength of the magnetic field within these jets. The simulations use a new non-equilibrium cooling method to produce synthetic emission maps in H[alpha] and [S II]. These are directly compared with multi-epoch Hubble Space Telescope (HST) observations of Herbig-Haro (HH) jets. There is excellent agreement between features seen in the simulations and the observations in terms of both proper motion and morphologies. Thus, YSO jets may be dominated by heterogeneous structures, and interactions between these structures and the shocks they produce can account for many details of YSO jet evolution"--Page v.