The Beam Dump eXperiment (BDX) is an electron-beam thick-target experiment aimed to investigate the existence of Light Dark Matter (LDM) particles in the MeV-GeV mass range. The experiment is expected to run at Jefferson Lab in a dedicated underground facility located 20 m downstream of the Hall A beam-dump, receiving up to $10^{22}$ 11 GeV electrons on target in $\sim1$ year time. The detector consists of a CsI(Tl) electromagnetic calorimeter (Ecal) and a veto system used to suppress the background. The expected signature of the DM interaction in the Ecal is a $\sim$ GeV electromagnetic shower paired with a null activity in the surrounding active veto counters. A complete small-scale prototype of the final detector has been built in order to validate the proposed technology and evaluate the cosmogenic background rejection capability. Beam-related background has been estimated by means of Monte Carlo (MC) simulations.This paper describes the BDX experimental setup and the results of the background studies along with the status and perspectives of the experiment.