The major issues confronting the performance of deep-UV (DUV) laser diodes (LDs) are reviewed along with the different approaches aimed at performance improvement. The impact of threading dislocations on the laser threshold current, limitations on heavy n- and p-doping in Al-rich AlGaN alloys, unavoidable electron leakage into the p-layers of (0001) LD structures, implementation of tunnel junctions, and non-uniform hole injection into multiple quantum wells in the active region are discussed. Special attention is paid to the current status of n- and p-type doping and threading dislocation density reduction, both being the factors largely determining the performance of DUV-LDs. It is shown that most of the above problems originate from intrinsic properties of the wide-bandgap AlGaN semiconductors, which emphasizes their fundamental role in the limitation of deep-UV LD performance. Among various remedies, novel promising technological and design approaches, such as high-temperature face-to-face annealing and distributed polarization doping, are discussed. Whenever possible, we provided a comparison between the growth capabilities of MOVPE and MBE techniques to fabricate DUV-LD structures.