Román Orús - Donostia International Physics Center In this talk I will make an overview of recent developments at my group on the modelling and simulation of a variety of strongly correlated systems with quantum-inspired tensor networks. Specifically, I will review our findings on the simulation of breathing Kagome antiferromagnets, 3d thermal bosons, 2d systems with SU(2) symmetry, and 2d/3d Kitaev models. Moreover, I will explain how the formalism can be extended to tackle other problems in other fields. In this respect, I will explain the case of the optimzation of dynamical trading trajectories for investment portfolios.