Short duration, high spatial coherence and the high intensity of pulses generated by X-ray FreeElectron Lasers (XFELs) enable unique experimental techniques in material studies, femtosecond chemistry and others. Crystal optics are widely used at XFELs as diagnostics devices and to tailor the pulses for the experiments. The diagnostics is required due to the random nature of XFEL pulses, which leads to each pulse having individual spectral properties. Strongly bent crystals allow to disperse various photon energies over angles thus allowing to measure the spectrum. In this thesis, the effect of diffraction on the bent crystal spectrometer is studied within the frame of dynamical diffraction. It is shown that the crystal thickness limits the resolving power of the device. Due to the high intensity of the pulses, the heating caused by the absorption in the crystals leads to a significant distortion of the lattice which affects the performance of optical devices based on crystal optics. A model for the estimation of the heat load effect on the performance of a cryo-cooled monochromator is presented. A wavefront simulation software is used to simulate the spatio-temporal effects of asymmetric dynamical diffraction.