The paper reports on elaboration of plasma‐assisted molecular beam epitaxy (MBE) of Al_xGa_1 − xN‐based quantum‐well (QW) structures with high Al content (up to 50% in the QW) grown directly on c‐sapphire. Different elements of the structure design are considered consecutively in detail along with the advanced growth approaches developed for each element. Special attention is paid to the growth conditions of (i) AlN nucleation layers with suppressed generation of threading dislocations (TDs), (ii) 2‐µm thick AlN buffer layers with atomically smooth droplet‐free morphology (rms = 0.46 nm) grown under the strongly metal‐rich conditions, (iii) cladding and waveguide AlGaN layers also possessing the atomically smooth droplet‐free morphology that is ensured by the accurately established phase diagram of metal(Ga)‐rich growth conditions within the temperature range 660–780 °C. Employing several 3‐nm thick strained GaN insertions in the AlN buffer layer and a AlGaN/AlN superlattice (SL) on top of it is shown to result in a significant decrease of TD's density down to 10⁸–10⁹ cm⁻² in the top QW region fabricated by a submonolayer digital alloying (SDA) technique. Finally, advanced AlGaN‐based QW structures are presented, which demonstrate optically pumped lasing within the deep‐ultraviolet (UV) wavelength range with the threshold power density below 600 kW cm⁻² (at 289 nm).