  We investigate great circle links in the three-sphere, the class of links
where each component is a great circle. Using the geometry of their
complements, we classify such links up to five components. For any two-bridge
knot complement, there is a finite cover that is the complement of a link of
great circles in $S^3$. We show that for many two-bridge knots, this cover
contains a closed incompressible surface. Infinitely many fillings of the
two-bridge knot lift to fillings of great circle link where the
incompressibility of this surface is preserved. Using this, we show that
infinitely many fillings of an infinite class of two-bridge knot complements
are virtually Haken.
