The original Riemann-Hilbert problem
is to construct a liner ordinary differential equation
with regular singularities whose solutions have a given monodromy.
Nowadays, it is formulated as a categorical equivalence
between the category of regular holonomic D-modules
and the category of perverse sheaves.
However it is a long standing problem to describe
holonomic D-modules with irregular singularities
in a geometric language.

Recently, I, with Andrea D'Agnolo, proved a Riemann-Hilbert correspondence
for holonomic D-modules which are not necessarily regular (arXiv:1311.2374).
In this correspondence,
we have to replace the derived category of constructible sheaves
with a full subcategory of ind-sheaves (or subanalytic sheaves)
on the product of the base space and the real projective line.