  Correlations play a crucial role in the nuclear many-body problem. We give an
overview of recent developments in nuclear structure theory aiming at the
description of these interaction-induced correlations by unitary
transformations. We focus on the Unitary Correlation Operator Method (UCOM),
which offers a very intuitive, universal and robust approach for the treatment
of short-range correlations. We discuss the UCOM formalism in detail and
highlight the connections to other methods for the description of short-range
correlations and the construction of effective interactions. In particular, we
juxtapose UCOM with the Similarity Renormalization Group (SRG) approach, which
implements the unitary transformation of the Hamiltonian through a very
flexible flow-equation formulation. The UCOM- and SRG-transformed interactions
are compared on the level of matrix elements and in many-body calculations
within the no-core shell model and with Hartree-Fock plus perturbation theory
for a variety of nuclei and observables. These calculations provide a detailed
picture of the similarities and differences as well as the advantages and
limitations of unitary transformation methods.
