  The Bose-Hubbard dimer Hamiltonian is a simple yet effective model for
describing tunneling phenomena of Bose-Einstein condensates. One of the
significant mathematical properties of the model is that it can be exactly
solved by Bethe ansatz methods. Here we review the known exact solutions,
highlighting the contributions of V.B. Kuznetsov to this field. Two of the
exact solutions arise in the context of the Quantum Inverse Scattering Method,
while the third solution uses a differential operator realisation of the su(2)
Lie algebra.
