"In recent years there has been a fast growing interest in Majorana fermions in condensed matter systems. These elusive particles, first predicted in the 1930s, are still awaiting experimental verification. It was recently realized that certain interacting systems in condensed matter physics hold a great promise for realizing Majorana fermions as emergent degrees of freedom. The candidate systems are known as topological superconductors. Vortices in these superconductors trap neutral zero energy Majorana modes, whose presence renders the exchange statistics ofthe host vortices non-Abelian. Interest in these states stems from the fundamental physics derived from this novel type of quantum statistics and from their possible use in future applications to fault-tolerant quantum computation. The main goal of the research described here is to devise methods to detect the presence of Majorana modes in topological superconductors. Three main objectives will be considered. The first is to detect the presence of Majorana modes via the non-Abelian vortex exchange statistics they give rise to; the behavior of Josephson vortices will be explored in arrays of superconducting islands to establish the mechanism through which they trap Majorana modes, with the aims to determine their coherence properties and to devise methods to coherently manipulate them. The second objective is to detect Majorana fermions using transport properties, particularly through their effect on noise and thermoelectric phenomena such as the Nernst coefficient. Finally, I will explore the effect of neutral modes on the dynamics following a quench in topological liquids, including their traces in the entanglement entropy. The candidate states that will be considered include strontium ruthenium oxide, the superconducting state of bismuth-selenide, the quantum Hall effect at filling factor 5/2 (which realizes a topological superconductor of composite fermions) and semiconductor-superconductor heterostructures."