The classical Riemann-Hilbert correspondence establishes an equivalence between the triangulated categories of regular holonomic D-modules and of constructible sheaves. In a joint work with Masaki Kashiwara, we proved a Riemann-Hilbert correspondence for holonomic D-modules which are not necessarily regular. The construction of our target category is based on the theory of ind-sheaves by Kashiwara-Schapira and is influenced by Tamarkin's work on symplectic topology. Among the main ingredients of our proof is the description of the structure of flat meromorphic connections due to Mochizuki and Kedlaya.[-]