We review some recent advancements we have obtained in tensor network
algorithms and their application to the study of correlated matter.
We present novel approaches to study abelian and non-abelian lattice
gauge theories, open many-body quantum systems and systems with
long-range interactions or periodic boundary conditions.
These novel approaches allowed us to obtain results on
a variety of phenomena hardly accessible before,
such as the Kibble-Zurek mechanism in Wigner
crystals, the out-of-equilibrium dynamics of the Schwinger model
and the phase diagram of the disordered Bose-Hubbard model.