One of the most compelling arguments motivating the search for physics beyond the Standard Model (SM) is the need to explain the nature of Dark Matter (DM). Despite an extensive experimental program that combined direct, indirect, and detection at colliders, to date, no conclusive results about DM particle nature have been determined. Among the DM models, those predicting DM particles in the sub-GeV mass range (also called Light Dark Matter or LDM) represent a theoretically well-grounded option if a new DM-SM interaction is introduced. A simple hypothesis considers a new feeble force transmitted by a vector boson $A^\prime$ (called Dark Photon), kinetically mixed with the ordinary photon. In this scenario, the $A^\prime$ can be generated in the SM interactions of charged particles and subsequently decays either into SM or LDM particles. The NA64-e experiment at CERN exploits the 100 GeV SPS electron beam impinging on a thick active target focusing mostly on the production and detection of the $A^\prime$ to LDM decay. If an $A^\prime$ is produced in the target, the LDM daughter particles leave the detector carrying away a significant amount of energy, resulting in a missing energy event. To date, NA64-e has collected $2.84\times10^{11}$ electrons on target. No events with missing energy greater than 50 GeV and no activity within the veto systems were observed. These results allowed the collaboration to set the most competitive limits in the LDM parameter space.