The Fractional Quantum Hall effect is one of the most fundamental phenomena of quantum physics. Under a very large magnetic field, and at fractional filling of a Landau level, when electrons are “supposed” (by simple band theory) to form a metal, one finds a gapped insulating state that is “topologically ordered” and hosts a huge array of interesting phenomena. Fractional excitations with abelian and non-abelian statistics, gravitational anomalies, topological entanglement entropy, hall viscosity, gapless edges described by complex conformal field theories are only some of the examples of profound physics that can be tested in a laboratory. Starting with the Chern insulator model of Haldane, which realized the integer quantum Hall state in zero field, predictions have been made for the existence of a Fractional Chern Insulator - the equivalent of a Fractional Quantum Hall state at zero magnetic field. In this colloquium we present new seminal developments that have allowed for the observation of this state, and present the theoretical developments that differentiate the Fractional Chern Insulator from the Fractional Quantum Hall state, as well as the bright future of this field.