  We first review some topics in the classical computational geometry of lines,
in particular the O(n^{3+\epsilon}) bounds for the combinatorial complexity of
the set of lines in R^3 interacting with $n$ objects of fixed description
complexity. The main part of this survey is recent work on a core algebraic
problem--studying the lines tangent to k spheres that also meet 4-k fixed
lines. We give an example of four disjoint spheres with 12 common real
tangents.
