  This is a short review on selected theory developments on Tensor Network (TN)
states for strongly correlated systems. Specifically, we briefly review the
effect of symmetries in TN states, fermionic TNs, the calculation of
entanglement Hamiltonians from Projected Entangled Pair States (PEPS), and the
relation between the Multi-scale Entanglement Renormalization Ansatz (MERA) and
the AdS/CFT or gauge/gravity duality. We stress the role played by entanglement
in the emergence of several physical properties and objects through the TN
language. Some recent results along these lines are also discussed.
