  The original Riemann-Hilbert problem asks to find a Fuchsian ordinary
differential equation with prescribed singularities and monodromy in the
complex line. In the early 1980's Kashiwara solved a generalized version of the
problem, valid on complex manifolds of any dimension. He presented it as a
correspondence between regular holonomic D-modules and perverse sheaves.
  The analogous problem where one drops the regularity condition remained open
for about thirty years. We solved it in the paper that received a 2024
Frontiers of Science Award. Our construction requires in particular an
enhancement of the category of perverse sheaves. Here, using some examples in
dimension one, we wish to convey the gist of the main ingredients used in our
work.
  This is a written account of a talk given by the first named author at the
International Congress of Basic Sciences on July 2024 in Beijing.
