Isomonodromic tau-functions corresponding to various special matrix Riemann-Hilbert problems turn out to be meromorphic sections of certain line bundles (as a rule of Hodge determinant line bundle) over underlying moduli spaces. This allows to use them to obtain (both new and old) relations between divisor classes on these moduli spaces (spaces of admissible covers, moduli spaces of holomorphic differentials on Riemann surfaces etc). We review these and other applications of such objects in the theory of random matrices, spectral geometry and Frobenius manifolds. The talk is based on joint works with A.Kokotov and P.Zograf.
