  We present a review of the Unitary Coupled Cluster (UCC) ansatz and related
ans\"atze which are used to variationally solve the electronic structure
problem on quantum computers. A brief history of coupled cluster (CC) methods
is provided, followed by a broad discussion of the formulation of CC theory.
This includes touching on the merits and difficulties of the method and several
variants, UCC among them, in the classical context, to motivate their
applications on quantum computers. In the core of the text, the UCC ansatz and
its implementation on a quantum computer are discussed at length, in addition
to a discussion on several derived and related ans\"atze specific to quantum
computing. The review concludes with a unified perspective on the discussed
ans\"atze, attempting to bring them under a common framework, as well as with a
reflection upon open problems within the field.
