  In this tutorial-style review we discuss basic concepts of coupled cluster
theory and recent developments that increase its computational efficiency for
calculations of molecules, solids and materials in general. We will touch upon
the connection between coupled cluster theory and the random-phase
approximation that is widely used in the field of solid-state physics. We will
discuss various approaches to improve the computational performance without
compromising on accuracy. These approaches include large-scale parallel design
as well as techniques that reduce the pre-factor of the computational
complexity. A central part of this article discusses the convergence of
calculated properties to the thermodynamic limit, which is of significant
importance for reliable predictions of materials properties and constitutes an
additional challenge compared to calculations of large molecules. We mention
technical aspects of computer code implementations of periodic coupled cluster
theories in different numerical frameworks of the one-electron orbital basis;
the projector-augmented-wave formalism using a plane wave basis set and the
numeric atom-centered-orbital (NAO) with resolution-of-identity. We will
discuss results and the possible scope of these implementations and how they
can help advance the current state of the art in electronic structure theory
calculations of materials.
