Given a knot in the 3-sphere with hyperbolic complement, one would like to try to understand the geometry of Seifert surfaces, essential surfaces with boundary the knot. In unusual cases, which we will discuss, such a surface can be totally geodesic (also called Fuchsian). The existence of such surfaces says a lot about the knot. However, much more common is for the surface to be quasi-Fuchsian. It turns out that many of the results know for Fuchsian surfaces can be extended to quasi-Fuchsian surfaces. Lots of pictures will be included. No familiarity with hyperbolic knots and surfaces will be assumed.