One of the most remarkable discoveries in physics of the last 50 years is the fractional quantum Hall effect. The Laughlin theory that generally accounts for this phase of matter, also implies that there are quasi-particles which are – in effect – a fraction of an electron. Theoretical proposals for interferometric methods that could directly confirm the existence and character of these expected “fractionalized” excitations were made soon after, but it is only in the last couple of years that these experiments have been successfully carried out in a variety of physical devices, beginning with a recent breakthrough experiment by Manfra and colleagues. In this talk, I will review the theory of quasi-particles with fractional charge and fractional statistics, and describe the recent experimental and theoretical progress that has allowed the new developments in the field.