The development in the field of X-ray laser and its applications at c-FAST is discussed in detail. First of all the recent progress in understanding of seeding X-ray laser with harmanics is presented. On the other hand, analysis of the kinetic processes by numerical simulations shows their dependence on the pump laser pulse structure. The latter cleary supports the thesis that multi-pulse pump schemes are more efficient that those based on two or
single laser pump pulse. Finally such applications as coherent diffraction imaging and photoelectron spectroscopy constitute basis for practical use of X-ray lasers.
High-harmonic-seeded x-ray laser became an important issue in x-ray laser development due to the possibility to obtain a
highly coherent and polarized soft x-ray source. We performed theoretical investigations into amplification of high
harmonic pulses in an x-ray lasing medium by using a model based on Maxwell-Bloch equations. From the theoretical
works, we analyze characteristics of energy extraction and temporal profile of output pulse. In addition, preliminary
experimental results and ongoing experiments related the harmonic-seeded x-ray lasers are reported.