  Given a point A in the real Grassmannian, it is well-known that one can
construct a soliton solution u_A(x,y,t) to the KP equation. The contour plot of
such a solution provides a tropical approximation to the solution when the
variables x, y, and t are considered on a large scale and the time t is fixed.
In this paper we give an overview of our work on the combinatorics of such
contour plots. Using the positroid stratification and the Deodhar decomposition
of the Grassmannian (and in particular the combinatorics of Go-diagrams), we
completely describe the asymptotics of these contour plots when |y| or |t| go
to infinity. Other highlights include: a surprising connection with total
positivity and cluster algebras; results on the inverse problem; and the
characterization of regular soliton solutions -- that is, a soliton solution
u_A(x,y,t) is regular for all times t if and only if A comes from the totally
non-negative part of the Grassmannian.
