Quantum computing promises to solve problems, which are impossible for classical computers. Among the different schemes of how to design a quantum computer, one particularly exotic version has raised a lot of attention lately. Although so-called topological quantum computing is a rather young concept, it promises to reduce the required overhead of physical quantum bits per logical quantum bit by a factor of 100-1000, due to an intrinsic protection against certain quantum errors. Once the fundamental mechanism - braiding of Majorana zero modes - is demonstrated, the topological scheme could become the most promising in terms of scalability. This article offers a short introduction to the topological concept and also aims to review the latest developments and efforts in this rapidly evolving field. In addition to this, it discusses different platforms for experimental realization of topologically protected devices. One particularly promising platform might evolve when in-situ fabrication techniques are applied to magnetically doped topological insulators. As a result, it should become possible to fabricate high fidelity Majorana devices for quantum computational tasks in a scalable fashion.