During the last years we have seen the birth of free-electron lasers, a new type of light source ten billion times brighter than syncrotrons and able to produce pulses only a few femtoseconds long. One of the main motivations for building these multi-million dollar machines was the prospect of imaging biological samples such as proteins and viruses in 3D without the need for crystallization or staining. This thesis contains some of the first biological results from free-electron lasers. These results include 2D images, both of whole cells and of the giant mimivirus and also con- tains a 3D density map of the mimivirus assembled from diffraction patterns from many virus particles. These are important proof-of-concept experiments but they also mark the point where free-electron lasers start to produce biologically relevant results. The most noteworthy of these results is the unexpectedly non-uniform density distribution of the internals of the mimivirus. We also present Hawk, the only open-source software toolkit for analysing single particle diffraction data. The Uppsala-developed program suite supports a wide range fo algorithms and takes advantage of Graphics Processing Units which makes it very computationally efficient. Last, the problem introduced by structural variability in samples is discussed. This includes a description of the problem and how it can be overcome, and also how it could be turned into an advantage that allows us to image samples in all of their conformational states.