In recent years, there have been advancements in the algebro-geometric construction of moduli spaces of parabolic connections and parabolic Higgs bundles on algebraic curves of arbitrary genus. We can show that generalized Riemann-Hilbert correspondences, which are maps from the moduli spaces of parabolic connections to the moduli spaces of monodromy and Stokes data, are surjective, proper birational analytic morphisms. This fact shows that the generalized monodromy-preserving deformations give rise to dynamical systems with geometric Painlevé properties on families of moduli spaces of parabolic connections. These moduli spaces are known to admit algebraic symplectic structures, and one has algebraic geometric constructions of Darboux coordinates for these symplectic structures. 

These developments  have allowed for a detailed treatment of integrable systems and dynamical systems arising from monodromy-preserving deformations in algebraic geometry.   Additionally, research has advanced on the relation between expansions of τ-functions of Painlevé equations and those constructed from conformal field theory and WKB analysis.  It is a highly intriguing research theme to investigate the connections between these theories and the theories of topological recursions and mirror symmetry.  Furthermore, research on discrete Painlevé systems and quantum Painlevé systems has been progressing, and the study of symmetries associated with these systems brings new perspectives in various fields.