X-ray radiation has been used to study structural properties of materials for morethan a hundred years. Construction of extremely coherent and bright X-ray radiationsources such as free electron lasers (FELs) and latest generation storage rings led torapid development of experimental methods relying on high radiation coherence.These methods allow to perform revolutionary studies in a wide range of fields fromsolid state physics to biology. In this thesis I focus on several important problemsconnected with the coherent methods.The first part considers applications of dynamical diffraction theory on crystals tostudies with coherent X-ray radiation. It presents the design of a high-resolution spectrometerfor free electron lasers that should allow to resolve spectral structure of individualFEL pulses. The spectrometer is based on the principle of dynamical diffractionfocusing. The knowledge of individual FEL pulse spectra is necessary for understandingFEL longitudinal coherence. In the same part I present quasi-kinematicalapproximation to dynamical theory which allows to treat analytically phase effectsobserved in X-ray coherent imaging on nanocrystals. These effects may play a bigrole when methods such as ptychography are used to study crystalline samples.The second part deals with measurements of FEL coherence properties using intensity- intensity interferometry. Results of several experiments performed at FELsFLASH and LCLS are revealed in this section. I have developed models and theoriesto explain the behavior observed in experiments on FLASH. These models allowedto extract information about external positional jitter of FEL pulses and secondarybeams present in FEL radiation. In the LCLS experiment the Hanbury Brown andTwiss type interferometry was performed on Bragg peaks from colloidal crystal. Thisdid not require additional measurements without the sample and information wasextracted directly from diffraction patterns. Therefore intensity-intensity interferometrycan in principle be used directly on sample diffraction patterns to understandstatistical behavior of the FEL during the measurements.Another problem that is considered in this thesis is the problem of electronic damagefrom bright FEL pulses. I have considered the effect of many ionization processeson single-particle imaging experiments on biological objects. Simulations were performedto understand the effect of shortening pulse durations and increasing intensitieson the diffraction pattern, its fluctuations from pulse to pulse and Comptonbackground. As a result of these simulations, bounds on the feasible intensities andpulse durations are suggested
