If neutrinos are Majorana particles, i.e. fermions that are their own antiparticles, then neutrinoless double-beta (0νββ) decay is possible. In such a process, two neutrons can simultaneously decay into two protons and two electrons without emitting neutrinos. Neutrinos being Majorana particles would explicitly violate lepton number conservation, and might play a role in the matter–antimatter asymmetry in the universe. The MAJORANA DEMONSTRATOR experiment is under construction at the Sanford Underground Research Facility in Lead, SD and will search for the neutrinoless double-beta (0νββ) decay of the ⁷⁶Ge isotope. The goal of the experiment is to demonstrate that it is possible to achieve a sufficiently low background rate in the 4 keV region of interest (ROI) around the 2039 keV Q-value to justify building a tonne-scale experiment. In this paper, we discuss the physics and design of the MAJORANA DEMONSTRATOR, its approach to achieving ultra-low background and the status of the experiment.