Topological superconductors are a novel class of quantum matter that host Majorana fermions (MFs), which are promising candidates for fault-tolerant topological quantum computing. So far, MFs have been extensively pursued in hybrid semiconductor-superconductor nanowires, where two MFs are expected to appear at the two ends of the nanowire in the presence of a large external magnetic field. Interestingly, MFs are also predicted to appear at the interface of a topological insulator (TI) and a s-wave superconductor (SC). In this talk, I will first briefly present our previous study on a SC-TI-SC junction (Josephson junction) as a promising platform to realize topological superconductivity and MFs. In these junctions, we observe an anomalous enhancement of the critical current at low temperatures, Aharonov-Bohm oscillations of the supercurrent, and a highly non-sinusoidal (skewed) current-phase relation. Our results suggest superconductivity is induced in the spin-helical topological surface states of our TIs and point toward nearly ballistic nature of superconducting transport. In the second part of the talk, I will discuss another emerging quantum system, i.e., a quantum anomalous Hall (QAH) insulator coupled to an s-wave superconductor, as a potential candidate to form “chiral Majorana edge modes”. A recent transport experiment considers the half-quantized two-terminal conductance plateau in a millimeter-size QAH – Nb hybrid structure as evidence for the chiral Majorana edge modes. However, there are concerns about this interpretation because non-Majorana mechanisms can also generate similar signatures, especially in a disordered QAH system. I will present our systematic study of the superconducting contact transparency and its influence on the two-terminal conductance measurements and provide a non-Majorana explanation for the appearance of the half-quantized plateau in the QAH – Nb hybrid structures. Finally, I will discuss the necessary conditions and the prospects of realizing MFs in a phase-coherent micrometer-sized QAH insulators.