Ricci-flat spaces are analogues of space-times satisfying Einstein's vacuum field equations of General Relativity. Unlike their flat cousins, these spaces exhibit fascinating geometric properties and are poorly understood. In odd dimensions the only non-trivial Ricci-flat spaces we can find are 7-dimensional and they appear in theoretical physics, making geometry in 7 dimensions particularly compelling to study. I will describe in an elementary way some of the recent endeavours to understand this geometry and several key open questions.