With stellar stream discoveries increasing dramatically in the past decade, a vast assortment of perturbed streams have allowed us to constrain properties of both baryonic structure in the halo along with the Milky Way history in general. In this thesis, I primarily pursue a promising aspect of streams of probing for dark matter substructure. The abundances and masses of dark matter substructure in galaxies is highly dependent on the nature of the dark matter particle, and streams may allow us to recover their properties, in turn better constraining the dark matter particle. In the process of this, I first demonstrate that by using mock streams generated in realistic Milky Way potentials, we can use observations of a perturbed stream track to recover subhalo properties. This includes present day realistic observations we can expect from photometric and spectroscopic data from Gaia and the Dark Energy Survey. This had only been demonstrated on circular orbits using the analytic impulse approximation prior to this. With this proof of concept shown, I explore how this can be done with real data including the ATLAS-Aliqa Uma stream, which has a very significant kink along its track with features in its radial velocities associated with it too. I improve upon typical likelihood estimation on streams using Kernel Density Estimation, to best consider their 2-dimensional on sky structure. While unsuccessful in producing quantitative fits, I reveal new styles of subhalo-stream interactions which can leave kink like features or spurs from very old impacts between subhaloes and streams. As a result, I show that the nature of a streams morphology and kinematics could potentially help decipher the nature of a potential subhalo-stream encounter. Additionally, I discuss additional parameters we should consider for future fits to these encounters to some real streams such as ATLAS-ALiqa Uma. Most important is likely the progenitor properties, which can affect properties such as the stream orientation, width and velocity dispersion. Finally, I explore how the Galactic bar and spiral structure, including a newer, more accurate bar model, could affect streams such as ATLAS-Aliqa Uma, which has an apocentre of ~40kpc but relatively close pericentre of ~13kpc. We confirm with previous work that they cannot produce the kink. On one instance though, they slightly influenced the orientation of the track. This could play a role in fitting streams as this could affect progenitor properties. While the focus of the work here is on fitting dark matter subhaloes due to the implications of the subhalo properties on constraining the dark matter particle, the findings of these baryonic structures hint at how streams could be used more in the future to in turn, provide better constraints on these structures.