In this proceeding, the author presents a very nice review on the use of tensor numerical methods for the approximation of the solution of high dimensional partial differential equations, with a special focus on tensor formats, like Tucker, Tensor-Train formats, and especially the quantized version of these formats. In the first section of the paper, the author introduces the main different tensor formats that are the most widely used in the literature for the approximation of functions and operators. The author puts an emphasis on the quantized version of these formats and the approximation properties they possess, which were proved by the author and coworkers in several works. These approximation properties are also illustrated on numerical examples. In the second section, the author presents how these quantized tensor methods can be used to solve high-dimensional PDEs. Two main examples of applications are provided: the first one deals with the approximation of the solution of the Hartree-Fock equation in electronic structure calculations, where one of the main numerical issue lies in the approximation of the electron integrals; the second one is concerned with the approximation of time-dependent parabolic equations, and especially here the chemical master equation.