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The talk is based on two facets of tensor networks. One is the ability to perform reasonably accurate numerical renormalization group transformations of spin systems and gauge theories based on ideas of higher-order singular value decomposition. Another is the description in terms of Matrix Product states (MPS) which furnishes an approximation to the ground state of the quantum spin chain with local Hamiltonian and enables us to study scattering in real-time away from integrable limits. The talk is based on the past (arXiv:1901.11443, arXiv: 2105.08066) and upcoming work.