Generalized Riemann-Hilbert correspondence: old and new

Aim of the talk is to overview some parts of the joint project with Maxim Kontsevich which is devoted to a generalization of the Riemann-Hilbert correspondence to arbitrary complex symplectic manifolds. We proposed it 10 years ago as a part of our program "Holomorphic Floer Theory". It relates categories of holonomic deformation-quantization modules and Fukaya categories in the framework of complex symplectic manifolds. I am going to discuss global and local aspects of the generalized RH-correspondence including (if time permits)  its relation to non-archimedean analytic geometry.