  This thesis contributes to the understanding of symmetry-enriched topological
phases focusing on their descriptions in terms of tensor network states. The
Projected Entangled Pair State (PEPS) formalism allows us to locally encode the
main properties of the models (like topological order, symmetries and their
interplay) in the tensors. We have used that encoding to classify, construct
and detect some classes of symmetry-enriched topological phases in 2D PEPS. For
that purpose, we have studied what the allowed freedom in the tensors
generating the same tensor network state is. These results are the so-called
'fundamental theorems' and they give the necessary knowledge to properly study
symmetries (actions that leave the states invariant). We focus our study on the
family of PEPS describing quantum double models of $G$, the so-called
$G$-injective PEPS, and on global on-site symmetries coming from a finite group
$Q$: as a result of the classification we have a finite number of phases
closely related to the theory of group extensions. We also provide the maps
that appear in group extension theory with physical meaning and we characterize
their actions on the ground subspace and on the anyons. We construct a
representative of each class of our classification. Moreover, we connect our
construction with an interesting physical phenomenon, the so-called anyon
condensation, which describes topological phase transitions. We have also
proposed a family of gauge invariant quantities and their corresponding order
parameters (in the form of expectation values of a local operator in 2D) to
detect the corresponding quantum phases, in particular their symmetry
fractionalization patterns. We conclude this thesis by touching on some
mathematical open problems in PEPS.
