2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/127438We first review some topics in the classical computational geometry of lines, in particular the O(n^{3+ε}) 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.22 pages, 13 color figuresMetric GeometryAlgebraic Geometry14N99; 14Q15; 52C45; 68U05text