I will outline the constant term method for solving certain classes of lattice path problems. The method has a rich combinatorial interpretation. I will show connections with transfer matrices, the Bethe Ansatz, eigenvectors, orthogonal polynomials, zero sums, partial fractions, Greens functions and the method of images. I will  also briefly mention two applications. The first is a model for traffic flow - the Simple Asymmetric Exclusion Model. This model also illustrates the occurrence of equilibrium phenomena occuring in non-equilibrium systems. The second application will be to a polymer system the solution of which is equivalent to solving a weighted random walk on a line segment.