Malliavin calculus and rough paths

The purpose of this note is to give a unified and streamlined presentation of Gaussian rough path theory (Coutin–Qian, Friz–Victoir) and its interactions with Malliavin calculus and Hörmander theory. The main result of [T. Cass, P. Friz, Densities for RDEs under Hörmanderʼs condition, Ann. of Math. (2) 171 (3) (2010) 2115–2141] is explained and we conclude with an outlook on open problems.