X-ray lasers are creating unprecedented research opportunities in physics,chemistry and biology. The peak brightness of these lasers exceeds presentsynchrotrons by 1010, the coherence degeneracy parameters exceedsynchrotrons by 109, and the time resolution is 105 times better. In theduration of a single flash, the beam focused to a micron-sized spot has the samepower density as all the sunlight hitting the Earth, focused to a millimetresquare. Ultrafast coherent X-ray diffractive imaging (CXDI) with X-ray lasers exploitsthese unique properties of X-ray lasers to obtain high-resolution structures fornon-crystalline biological (and other) objects. In such an experiment, thesample is quickly vaporised, but not before sufficient scattered light can berecorded. The continuous diffraction pattern can then be phased and thestructure of a more or less undamaged sample recovered% (speed of light vs. speed of a shock wave).This thesis presents results from the first ultrafast X-ray diffractive imagingexperiments with linear accelerator-driven free-electron lasers and fromoptically-driven table-top X-ray lasers. It also explores the possibility ofinvestigating phase transitions in crystals by X-ray lasers. An important problem with ultrafast CXDI of small samples such as single proteinmolecules is that the signal from a single measurement will be small, requiringsignal enhancement by averaging over multiple equivalent samples. We present anumerical investigation of the problems, including the case where samplemolecules are not exactly identical, and propose tentative solutions. A new software package (Hawk) has been developed for data processing and imagereconstruction. Hawk is the first publicly available software package in thisarea, and it is released as an open source software with the aspiration offostering the development of this field.

The newly emerging technology of X-ray free-electron lasers (XFELs) has the potential to revolutionise molecular imaging. XFELs generate very intense X-ray pulses and predictions suggest that they may be used for structure determination to atomic resolution even for single molecules. XFELs produce femtosecond pulses that outrun processes of radiation damage and permit the study of structures at room temperature and of structural dynamics. While the first demonstrations of flash X-ray diffractive imaging (FXI) on biological particles were encouraging, they also revealed technical challenges. In this work we demonstrated how some of these challenges can be overcome. We exemplified, with heterogeneous cell organelles, how tens of thousands of FXI diffraction patterns can be collected, sorted, and analysed in an automatic data processing pipeline. We improved  image resolution and reduced problems with missing data. We validated, described, and deposited the experimental data in the Coherent X-ray Imaging Data Bank. We demonstrated that aerosol injection can be used to collect FXI data at high hit ratios and with low background. We reduced problems with non-volatile sample contaminants by decreasing aerosol droplet sizes from ~1000 nm to ~150 nm. We achieved this by adapting an electrospray aerosoliser to the Uppsala sample injector. Mie scattering imaging was used as a diagnostic tool to measure positions, sizes, and velocities of individual injected particles. XFEL experiments generate large amounts of data at high rates. Preparation, execution, and data analysis of these experiments benefits from specialised software. In this work we present new open-source software tools that facilitates prediction, online-monitoring, display, and pre-processing of XFEL diffraction data. We hope that this work is a valuable contribution in the quest of transitioning FXI from its first experimental demonstration into a technique that fulfills its potentials.