Sarnak’s Möbius disjointness conjecture speculates that the Möbius sequence is disjoint to all topological dynamical systems of zero topological entropy. In this talk we will discuss several special cases of this conjecture obtained by applying a number-theoretical theorem of Matomäki-RadziwiÅ‚Å‚-Tao to dynamical settings. Part of the talk is based on joint work with Wen Huang and Guohua Zhang.