Progress in the research devoted to developing x-ray lasers will be reviewed as it pertains to one-electron hydrogenic ions created and pumped to inversion in high-density laser-produced plasmas. A simple analysis defines a useful parameter space. Measured gain coefficients for C5+ are in good agreement with modeling for electron-capture pumping. Photon pumping is identified for possible circumvention of radiative-trapping limitations in larger volumes. Preliminary data on aluminum appear promising for shorter wavelength extrapolation. The advantage of efficient x-ray cavities is apparent. Extension of the illustrative analysis provides directions for future quantitative measurements leading to large scale gain experiments.