Lattice paths and (bi)orthogonal polynomials

It is well-known (at least in principle...) that the enumeration of Motzkin-type paths is intimately related to the theory of orthogonal polynomials, via Xavier Viennot's corresponding combinatorial theory. It is perhaps less well-known (at least, this was the case for me until recently) that the enumeration of Schr\"oder-like paths is intimately related to the theory of biorthogonal polynomials, via a recent combinatorial theory developed by Shuhei Kamioka. My plan is to start with a review of Viennot's combinatorial theory of orthogonal polynomials and then present Kamioka's combinatorial theory of biorthogonal polynomials.