Quasi-Fuchsian manifolds are hyperbolic manifolds of topological type Σ × R with well-behaved ends. They provide a setting where the underlying topology is simple but the geometry can be very intricate. Uhlenbeck defined a sub-class of quasi-Fuchsian manifolds M that contain minimal surfaces with maximum principal curvature λ_0 < 1, proved that any such surface is unique, and gave a way of parametrizing this sub-class in terms of data attached to this unique minimal surface. Such M are called almost-Fuchsian and have been well-studied since. After describing the basic landscape I will talk about joint work with Zeno Huang that constructs a compactification of the almost Fuchsian space. As a corollary we can prove a gap theorem for the geometry of minimal surfaces in hyperbolic 3-manifolds M that fiber over the circle. I will go over some aspects of the proofs and the much that remains to be understood.