Results of recent semi-analytical and three dimensional computational fluid dynamics (3D CFD) modeling of supersonic diode pumped alkali lasers (DPALs), as well as summary of work in progress, are reported. DPALs have been extensively studied in the past few years and static and flowing-gas devices have been investigated. Modeling of these devices has been conducted as well and fluid dynamics and kinetic processes have been taken into account, but until recently only flowing-gas DPALs with subsonic velocity of the gas were considered. Following our previous work on supersonic DPALs we further explore in the present study the feasibility of operating DPALs with supersonic expansion of the gaseous laser mixture, consisting of alkali atoms, He atoms and (frequently) hydrocarbon molecules. The motivation for this exploration stems from the possibility of fast and efficient cooling of the mixture by the supersonic expansion. In a recent paper (S. Rosenwaks et al, Proc. SPIE 8962, 896209 (2014)) we have reported on semi-analytical modeling for a supersonic Cs DPAL with parameters similar to those of the 1-kW flowing-gas subsonic Cs DPAL (A.V. Bogachev et al, Quantum Electron. 42, 95 (2012)); the maximum power, Plase, for the former was found to be higher than for the latter by 25%. Optimization of the He/CH4 buffer gas composition and flow parameters using 3D CFD modeling shows that for Bogachev et al resonator parameters, extremely high lasing power and optical-to-optical efficiency, 33 kW and 82%, respectively, are achievable in the Cs supersonic device. Comparison between the semi-analytical and the 3D CFD models for Cs shows that the latter predicts much higher maximum achievable laser power than the former. For a supersonic K DPAL the semi-analytical model predicts Plase = 43 kW, 70% higher than for subsonic with the same resonator and K density at the inlet, the maximum optical-to-optical efficiency being 82%. The paper also includes estimates for closed cycle supersonic systems.