The Kitaev model has been studied extensively in recent years due to its connection with Majorana fermions and non-trivial quantum statistics. The model consists of spin-1/2's at the sites of a honeycomb lattice with highly anisotropic interactions between nearest neighbors. It is one of the few quantum spin models known in two dimensions which are exactly solvable. The Hamiltonian has a large number of conserved quantities. The solution consists of mapping the spin-1/2's to non-interacting Majorana fermions. The model exhibits many interesting properties such as the extremely short-ranged spin correlation functions and the way the correlations are modified if the parameters of the Hamiltonian are changed with time. It is also instructive to look at a large spin (semiclassical) version of the model. This is not exactly solvable although it has the same conserved quantities. This system provides an example of quantum fluctuations (spin wave zero point energy) reducing a large classical degeneracy of the ground state to a smaller quantum degeneracy.