We give an introduction to recent developments in the geometry of compact manifolds with exceptional holonomy, focusing on recent work with Corti, Nordstrom and Pacini; we prove the existence of many compact 7-manifolds with holonomy G2 that contain rigid associative submanifolds. The main ingredients in the proof are: an appropriate noncompact version of the Calabi conjecture, gluing methods and a certain class of complex projective 3-folds (weak Fano 3-folds).