The tensor product methodology is one of data compression approaches in mathematical modelling, based mainly on linear algebra. Tensor decompositions offer potentially a significant reduction of the computational burden…sometimes cracking problems with 10100 or more unknowns that seem otherwise unsolvable. However, as many data-driven techniques, tensor methods are only good if the application under consideration allows that. We found positive examples in uncertainty quantification , stochastic dynamical systems (Fokker-Planck [16,13], and master [5,7] equations), quantum modelling (Schroedinger [9,8] and Liouville-von Neumann  equations). Surely, the numerical efficiency depends on all components of the scheme. Sometimes we also needed to develop a better preconditioner [18,3]. The tensor product formalism is also applicable to some nonlinear problems [2, 11].
More details below are structured in the following categories