A theta graph, denoted T(a,b,c), consists of a pair of vertices together with three disjoint paths between the vertices of lengths a, b, and c. In this talk, we characterize graphs which exclude certain theta graphs as a minor. We begin with small theta graphs, in particular those with at most 7 edges. This work is part of a larger project which characterizes H-minor-free graphs for all 2-connected graphs H on at most 7 edges and is joint with Mark Ellingham, Tom McCourt, and Tony Nixon. Next we look at excluding large theta graphs. We allow at least one of the paths to be arbitrarily long. The most complicated case is excluding T(t,t,t) where t is any large integer. The work on large theta graphs is joint with Guoli Ding.