Topological Insulators (TI) are a novel class of materials that are ideally insulating in the bulk, but have gapless, metallic states at the surface. These surface states have very exciting properties such as suppressed backscattering and spin-momentum locking, which are of great interest for research efforts towards dissipation-less electronics and spintronics. The popular thermo-electrics from the Bi chalcogenide family -- Bi2Se3 and Bi2Te3 -- have been experimentally demonstrated to be promising candidate TI materials, and form the chosen material system for this dissertation research. The first part of this dissertation research focuses on low temperature magneto-transport measurements of mesoscopic topological insulator devices (Chapter 3). The top-down patterning of epitaxial thin films of Bi2Se3 and Bi2Te3 (that are plagued with bulk conduction) is motivated, in part, by an effort to enhance the surface-to-volume ratio in mesoscopic channels. At cryogenic temperatures, transport measurements of these devices reveal periodic conductance fluctuations in straight channel devices, despite the lack of any explicit patterning of the TI film into a ring or a loop. A careful analysis of the surface morphology and comparison with the transport data then demonstrate that scattering off the edges of triangular plateaus at the surface leads to the creation of Aharonov-Bohm electronic orbits responsible for the periodicity. Another major focus of this dissertation work is on combining topological insulators with magnetism. This has been shown to open a gap in the surface states leading to possibilities of magnetic "gating" and the realization of dissipation-less transport at zero-field, amongst several other exotic quantum phenomena. In this dissertation, I present two different schemes for probing these effects in electrical transport devices -- interfacing with insulating ferromagnets (Chapter 4) and bulk magnetic doping (Chapter 5). In Chapter 4, I shall present the integration of GdN with Bi2Se3 thin films. Careful structural, magnetic and electrical characterization of the heterostructures is employed to confirm that the magnetic species is solely restricted to the surface, and that the ferromagnetic GdN layer to be insulating, ensuring current flow solely through the TI layer. We also devise a novel device geometry that enables direct comparison of the magneto-transport properties of TI films with and without proximate magnetism, all, in a single device. A comparative study of weak anti-localization suggested that the overlying GdN suppressed quantum interference in the top surface state. In our second generation hetero-structure devices, GdN is interfaced with low-carrier density, gate-tunable thin films of (Bi,Sb)2Te3 grown on SrTiO3 substrates. These devices enable us to map out the comparison of magneto-transport, as the chemical potential is tuned from the bulk conduction band into the bulk valence band.In a second approach to study the effects of magnetism on TI's, I shall present, in Chapter 5, our results from magnetic doping of (Bi,Sb)2Te3 thin films with Cr -- a system that was recently demonstrated to be a Quantum Anomalous Hall (QAH) insulator. In a Cr-rich regime, a highly insulating, high Curie temperature ferromagnetic phase is achieved. However, a careful, iterative process of tuning the composition of this complex alloy enabled access to the QAHE regime, with the observation of near dissipation-less transport and perfect Hall quantization at zero external field. Furthermore, we demonstrate a field tilt driven crossover between a quantum anomalous Hall phase and a gapless, ferromagnetic TI phase. This crossover manifests itself in an electrically tunable, giant anisotropic magneto-resistance effect that we employ as a quantitative probe of edge transport in this system.