In 2012 several experiments reported evidence of the existence of Majorana states in semiconductor wires. They attracted a lot of interest since these peculiar states might be the basis of topological quantum computers whose operation principle is the dynamical braiding of linear chains of states. In this seminar I will give a general motivation on Majorana modes, focusing next on the description of their physics using a simple model of a semiconductor nanowire with Rashba spin-orbit interaction, induced superconductivity and Zeeman splitting. I will report on three different aspects: a) the spectrum of an isolated finite nanowire, b) the edge states of a semi infinite nanowire, c) the linear conductance of a finite nanowire attached to normal leads.