I will explain how to express the space of almost complex structures J(M) on a six-manifold M as the quotient of a space of sections of a sphere bundle over M by an S^1 action. This leads to a computation of the rational homotopy type of J(M) in most cases, as well as a simple description of the homotopy type in others, such as when M is the six-sphere. In dimension 6, two orthogonal, almost complex structures generically intersect at a finite number of points inside twistor space. I will give a formula for the intersection number and discuss some applications. This is all joint work with Aleksandar Milivojevic.