Topological materials such as topological insulators and Weyl semimetals host exotic electronic states that emerge from nontrivial band topology. A key scientific challenge is to experimentally probe the magneto-optical signatures of these materials, especially when time-reversal symmetry is broken. In such cases, magnetism can significantly influence the low energy electrodynamics, giving rise to phenomena such as the anomalous Hall effect, spin-to-charge conversion, and circular dichroism. Understanding these effects is essential for both fundamental physics and the development of topological spintronic devices. In this dissertation, we employ terahertz (THz) and near-infrared (NIR) spectroscopies to investigate magnetic topological materials. We developed a time-domain THz transmission polarimetry system using photoconductive antennas, enabling precise measurements of polarization rotation in the 0.1–3.0 THz range. This system was applied to Cr-doped (Bi,Sb)2Te3, MnBi2Te4, and Co2MnGa, where we measured Faraday and Kerr effects and extracted complex optical conductivities. In parallel, we used THz emission spectroscopy based on electro-optic sampling to probe photocurrent dynamics. We observed helicity-dependent photocurrents in Co2MnGa and strong spin-to-charge conversion in magnetic/topological heterostructures. Additionally, circular dichroism microscopy was employed to study Eu2Ir2O7, a candidate magnetic Weyl semimetal with noncollinear antiferromagnetism, revealing significant circular dichroism attributed to a magnetic octupole moment. These measurements revealed several important findings. We demonstrated that the large anomalous Hall conductivity in Cr-doped (Bi,Sb)2Te3 and Co2MnGa originates from intrinsic Berry curvature effects. In MnBi2Te4, we observed a quantized anomalous Hall effect in thin films. In heterostructures, we identified efficient THz spin-to-charge conversion. And in Eu2Ir2O7, we linked the observed dichroism to topological band structure. Overall, this work advances our understanding of the interaction between topology and magnetism and establishes time-domain THz and nonlinear optical spectroscopies as powerful tools for probing emergent phenomena in topological quantum materials.