Ettore Majorana, in his short life, unintendedly has uncovered the most profound problem in quantum computation by his discovery of Majorana fermion, a particle which is its own anti-particle. Owing to its non-Abelian exchange statistics, Majorana fermions may act as a qubit for a universal quantum computer which is fault-tolerant. The existence of such particle is predicted in mid-gap states (zero modes) of a topological superconductor as bound states that have a highly entangled degenerate ground state. This introductory overview will focus on the simplest theoretical proposals of Majorana fermions for topological quantum computing in superconducting systems, emphasizing the quest from the scalability problem of quantum computer to its possible solution with topological quantum computer employing non-Abelian anyons on various platforms of certain Majorana fermion ‘signature’ encountered.

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