The thesis consists of three related projects where attempts have been made to simulate X-Ray Absorption (XAS) spectra of water and hexagonal ice, static non-resonant X-ray Emission (XES) spectrum of water and to apply the semi-classical approximation to Kramers-Heisenberg formula (SCKH) formalism to calculate the non-resonant XES spectrum of water and methanol. The first project is devoted to an investigation of the performance of damped response theory in combination with the DFT electronic structure method (CPP-DFT) in XAS spectrum simulations of liquid water. Based on this study the basis set and cluster size have been determined. The summed CPP-DFT XAS water spectrum was able to reproduce well the three main water absorption spectrum features – pre, main and post edge. The investigation of the CPP-DFT approach in case of hexagonal ice reveals that neither of four tested ice models with gradually increased degree of structural disorder can reproduce correctly the hexagonal ice spectrum features. A critical investigation of the available experimental ice spectra showed that those spectra are quite different depending on the sample preparation procedure and registration mode. This leads to questioning which ice structures have been actually measured. This was investigated using a Reverse Monte-Carlo based technique which fits the reference spectra using a library of pre-computed structures and assigns weights to each structure. The obtained weights were then used to generate the corresponding radial distribution functions (RDFs). The calculated RDFs have peaks corresponding to perfect lattice distances, but significantly broader than expected for the ideal lattice. In conclusion it was suggested that the available XAS ice spectra do not correspond to the perfect hexagonal ice, but rather samples with varying fraction of defects and possible impurity of amorphous ice. Simulation of the static non-resonant XES spectrum of water has been performed based on time-dependent density functional theory with the Tamm-Dancoff approximation (TD-DFT/TDA) level of theory. The simulation reveals that the 1b1 peak position is sensitive to the number of H-bonds and to the tetrahedrality of the environment as measured by the local structure index (LSI). The 1b1 peak splitting is observed between two structure sets – tetrahedrally coordinated, low density liquid (LDL) like, structures and asymmetric, high density liquid (HDL) like, structures. The magnitude of the peak splitting depends also on the H-bond lengths. A maximum value 0.6 eV is obtained between LDL structures with short bonds (< 2.68 Å) and HDL structures with long bonds (> 2.8 Å). The influence of core-hole induced dynamics on the spectrum profile has been studied based on the SCKH approximation for liquid water and methanol. The lone pair 2aʺ peak splitting in liquid methanol was explained based on methanol molecules in different H-bond coordination. The low energy 2aʺ peak is assigned to strongly H-bonded methanol molecules while weakly bonded or non-bonded methanol molecules contribute mainly to the high energy 2aʺ peak. The 2aʺ peak splitting is observed in the static XES spectrum, while inclusion of the core-hole induced dynamics preserves the split and does not generate additional spectrum features, but broadens and smears out spectrum features seen in the static case. Inclusion of the dynamical effects in the water case has revealed that the 1b1 peak splitting is preserved for LDL structures with short bonds and HDL structures with long bonds while unbalanced water structures with odd number of H-bonds generate peaks in between these two extreme cases.