Arithmetic link complements

In his 1982 Bulletin Article, Qn 19 of the problem list, Thurston posed: "Find topological and
geometric properties of quotient spaces of arithmetic subgroups of PSL(2,C). These manifolds
often seem to have special beauty." Arithmetic link complements in the 3-sphere provide some
particularly interesting examples of this. In this talk we take up this theme, compare and contrast
with dimension 2, and report on some recent work.