What makes up most of the Universe mass? - is the central question of modern science. A possible answer to this question is: It is thermal dark matter (DM) with mass below the electroweak scale, m_DM << 100 GeV. The NA64 experiment is a fixed-target experiment designed to search for light dark matter and sub-GeV New Physics in missing energy events from high-energy electron, muon and hadron interactions in an active target at the CERN SPS. In this talk, I will discuss the motivation for light dark matter, describe in details the NA64 concept and performance.

I will also present the latest NA64 results and discuss projections of the expected sensitivities from running after LHC long shutdown 2 and beyond.