The unknotting number of a knot $K$, denoted $u(K)$, is the minimum number of times the knot must pass through itself to result in the unknot. Determining unknotting numbers is a widely studied and subtle problem. Unknotting number can be extended to (abstractly planar) spatial graphs in a natural way. In this talk we will explain what known about unknotting numbers for spatial graphs, and how this relates to what is known for knots. We will also look at the connections with knotting in DNA, and unknotting numbers of knotoids.