Thurston's geometrization conjecture, proved by Perelman in 2003, states that every three-dimensional manifold can be cut into a collection of pieces, each of which has one of eight geometries. These "Thurston geometries" include the euclidean, spherical, and hyperbolic geometries, the products of the two-dimensional spherical and hyperbolic geometries with the euclidean line, and three other, stranger geometries. In this talk, I'll describe joint work with Rémi Coulon, Sabetta Matsumoto, and Steve Trettel, in which we simulate the "inside view" from within each of the Thurston geometries. That is we generate images assuming that light travels along geodesics in the geometry of the manifold.