I will present results on the tensorization problem of first order Sobolev spaces defined on metric measure spaces. For a general Sobolev exponent the tensorization of weak differentiable structures leads to a tensorization result where one of the factors is assumed to be a PI-space. When the Sobolev exponent is 2 we can make use of the tensorization property of Dirichlet forms and obtain the tensorization for spaces where the Sobolev norm is equivalent to a norm given by a Dirichlet form. Such spaces include infinitesimally Hilbertian spaces and spaces with finite Hausdorff dimension. This is joint work with Sylvester Eriksson-Bique and Elefterios Soutanis.