Logarithmic Sobolev inequalities (LSI) were first introduced by Gross in the 70's, and later found rich connections to geometry, probability, graph theory, optimal transport as well as information theory. In recent years, logarithmic Sobolev inequalities for quantum Markov semigroups have attracted a lot of attention and found applications in quantum information theory and quantum many-body system. For classical Markov semigroup on a probability space, an important advantage of log-Sobolev inequalities is the tensorization property that if two semigroups satisfies LSI, so does their tensor product semigroup. Nevertheless, tensoraization property fails for LSI in the quantum cases. In this talk, I'll present some recent progress on tensor stable log-Sobolev inequalities for quantum Markov semigroups. \\ \\ This talk is based on joint works with Michael Brannan, Marius Junge, Nicholas LaRacuente, Haojian Li and Cambyse Rouze.