A strong geometry with torsion corresponds to a Riemannian manifold carrying a metric connection with closed skew-symmetric torsion. When this connection has reduced holonomy group H, then we say that the underlying H-structure is strong. This notion of strong geometry with torsion has been predominantly studied in the context of Hermitian geometry, i.e. when H=U(n); such manifolds are known as strong Kahler with torsion (SKT) or pluriclosed manifolds. In this talk, I will discuss the corresponding notion in the context of G2 geometry and present some new results. This is based on a joint work with Anna Fino.