Topological states of matter are exotic quantum phases characterized by global geometric properties that remain robust against local perturbations. Topological insulator (TI) is an example of topological states with time-reversal symmetry. Breaking time-reversal symmetry in topological insulators via magnetism can lead to new topological states including quantum anomalous Hall (QAH) state, axion insulator state, and chiral topological superconductivity (TSC). These magnetic topological systems provide an appealing platform for exploring the interplay between electromagnetism, topology, and magnetic orders. Here I will summarize my theoretical works on the linear and nonlinear physical responses in magnetic topological materials, including QAH insulators with tunable Chern numbers, even-odd effect in intrinsic topological magnet MnBi2Te4, nonlinear Hall effect in magnetic TIs, pseudo circular photogalvanic effect in magnetic Weyl semimetals, and topological superconductivity in magnetic TI/FeTe heterostructures.