G2 manifolds constitute a class of Einstein seven-manifolds and are of substantial interest both in Riemannian geometry and theoretical physics. At present a vast number of compact G2 manifolds is known to exist. In this talk I will discuss a gauge-theoretic approach to the construction of invariants of compact G2 manifolds. I will focus on an interplay between gauge theories in dimensions 7 and 3 and how this can be used for the construction of the invariants.