In this defense, I will focus on my Ph.D. research, which spans from the investigation of three-dimensional (3D) quantum anomalous Hall (QAH) insulators to the exploration of topological superconducting (TSC) phase in topological insulator (TI) heterostructures. The QAH insulator is a material in which the quantum Hall effect appears under zero magnetic field. In the first half of my talk, I will introduce the thickness-dependent scaling behaviors in QAH insulators, which we attribute to the evolution of inter/intra-layer couplings. I will next briefly introduce our recent progress on the high Chern number QAH effect and QAH junctions. In the second half of my talk, I will first discuss possible pathways to detect Marana physics in TI/superconductor and QAH/superconductor heterostructures. I will then focus on the nanofabrication of TI-based Josephson junction devices and electrical transport measurements on these devices. Our results suggest that the vortex generation in these devices is probably mediated by TI’s Dirac surface states.