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).