  We introduce a notion of bipartite minors and prove a bipartite analog of
Wagner's theorem: a bipartite graph is planar if and only if it does not
contain $K_{3,3}$ as a bipartite minor. Similarly, we provide a forbidden minor
characterization for outerplanar graphs and forests. We then establish a
recursive characterization of bipartite $(2,2)$-Laman graphs --- a certain
family of graphs that contains all maximal bipartite planar graphs.
