Fluxonium consists of a superconducting loop interrupted by over 100 Josephson junctions, strips of insulating material AlOx a few nanometers thick sandwiched between superconducting Al layers. Consequently, the loop has an exceptionally large value inductance, which makes fluxonium distinct and useful. Having so many junctions per qubit has been generally viewed as a liability for establishing long coherence times. Yet, we observed coherence in excess of 1 millisecond and conclude that even longer coherence time should be possible by upgrading our fabrication procedures to the state of the art. We discuss how the exceptional combination of fluxonium's high coherence and strong anharmonicity can be utilized for improving the fidelity of logical gates and constructing analog simulators of strongly interacting quantum spin models.