Recent progress of laser frequency stabilization and the problems in achieving a high degree of reproducibility are discussed. Stability, resettability and reproducibility of the He-Ne laser either locked in its Lamb dip or in the inverted Lamb dip due to saturated absorption of pure neon in the cavity are reviewed. The advantages of molecular absorption lines are demonstrated theoretically and experimentally. An absorption line of methane at the 3.39μm He-Ne laser wavelength has a potential accuracy of 10-13 or better as an absolute standard of wavelength. Recent observation of the inverted Lamb dip and stabilization on the methane line by Hall and studies with other molecules are described.