Topological superconducting systems are intriguing physical systems in which an elusive class of fermions— Majorana fermions, whose antiparticles are themselves, can be created and used to construct topological qubits for quantum computing. Here I report on the realization and quantum transport measurements of topological superconducting quantum devices made from semiconductor nanostructures. The talk will be divided into two parts. In the first part, our study of topological superconducting quantum devices made from InSb nanowires and s-wave Nb superconductors will be reported and discussed. In each of the devices, a quantum dot is fabricated between two topological superconducting InSb nanowires. Both a zero conductance peak arising from Majorana fermions located at two outer ends of the two nanowires and two side conductance peaks arising from the interaction between the two inner Majorana fermions in the vicinity of the quantum dot are observed. In the second part of my talk, our very recent work on topological quantum devices made from InSb nanoplates and s-wave Al superconductors will be reported and discussed. Here, I will show that it is possible to turn the semiconductor InSb nanoplates into two-dimensional topological insulators. As a consequence, in a Josephson junction made from an InSb nanoplate in the topological phase, the measured supercurrent as a function of magnetic field shows an interference pattern which is in accordance with the transport through the edges of the nanoplate. Finally, future directions of the field and perspective applications of topological superconducting quantum devices in the quantum information technology will be discussed.