  Nanostructures with open shell transition metal or molecular constituents
host often strong electronic correlations and are highly sensitive to atomistic
material details. This tutorial review discusses method developments and
applications of theoretical approaches for the realistic description of the
electronic and magnetic properties of nanostructures with correlated electrons.
First, the implementation of a flexible interface between density functional
theory and a variant of dynamical mean field theory (DMFT) highly suitable for
the simulation of complex correlated structures is explained and illustrated.
On the DMFT side, this interface is largely based on recent developments of
quantum Monte Carlo and exact diagonalization techniques allowing for efficient
descriptions of general four fermion Coulomb interactions, reduced symmetries
and spin-orbit coupling, which are explained here. With the examples of the Cr
(001) surfaces, magnetic adatoms, and molecular systems it is shown how the
interplay of Hubbard U and Hund's J determines charge and spin fluctuations and
how these interactions drive different sorts of correlation effects in
nanosystems. Non-local interactions and correlations present a particular
challenge for the theory of low dimensional systems. We present our method
developments addressing these two challenges, i.e., advancements of the
dynamical vertex approximation and a combination of the constrained random
phase approximation with continuum medium theories. We demonstrate how
non-local interaction and correlation phenomena are controlled not only by
dimensionality but also by coupling to the environment which is typically
important for determining the physics of nanosystems.
