In the past decade, magnetic topological insulators have been an important focus in condensed matter physics research. The intricate interplay between the nontrivial band topology and spin, orbit, charge, and dimensionality degrees of freedom can give rise to abundant exotic topological quantum states and topological phase transitions. Measuring the transport properties of magnetic topological insulators is a crucial approach to exploring their exotic properties, which is of significant scientific importance in deepening our understanding of topological quantum states. Simultaneously, it also holds substantial potential applications in the development of novel low-power electronic devices. In this work, experimental progress of transport researches of magnetic topological insulators is reviewed, including quantum anomalous Hall effect and topological quantum phase transitions in magnetically doped topological insulators, the quantum anomalous Hall phase, axion insulator phase and Chern insulator phase in intrinsic antiferromagnetic topological insulator MnBi₂Te₄, as well as the helical phase emerged from the Chern insulator in pulsed high magnetic fields. Finally, this work analyzes the future direction of development in magnetic topological insulators, and the transport phenomena that have not been understood in these systems, offering an insight into and perspectives on the potential breakthroughs to be achieved in this area of research.