A review of theoretical works on the laboratory X-ray laser (XRL) rese
arch performed at RFNC- VNIITF for the last few years is presented. Th
ree potential photopumped XRL schemes with relatively short laser wave
lengths (44, 23, and 64 Angstrom) have been investigated. Theoretical
studies of lasing plasma parameters for some of the published recombin
ation and resonantly photopumped XRL schemes have been performed using
our kinetics and line-profile codes.