Biological samples are highly radiation sensitive. The rapid progress of their radiation damage prevents accurate structure determination of single macromolecular assemblies in standard diffraction experiments. However, computer simulations of the damage formation have shown that the radiation tolerance might be extended at very high intensities with ultrafast imaging such as is possible with the presently developed and operating x-ray free-electron lasers. Recent experiments with free-electron lasers on nanocrystals have demonstrated proof of the imaging principle at resolutions down to 1.6 Angstroms. However, there are still many physical and technical problems to be clarified on the way to imaging of single biomolecules at atomic resolution. In particular, theoretical simulations try to address an important question: How does the radiation damage progressing within an imaged single object limit the structural information about this object recorded in its diffraction image during a 3D imaging experiment? This information is crucial for adjusting pulse parameters during imaging so that high-resolution diffraction patterns can be obtained. Further, dynamics simulations should be used to verify the accuracy of the structure reconstruction performed from the experimental data. This is an important issue as the experimentally recorded diffraction signal is recorded from radiation-damaged samples. Photonics 2015, 2 257 It also contains various kinds of background. In contrast, the currently used reconstruction algorithms assume perfectly coherent scattering patterns with shot noise only. In this review paper, we discuss the most important processes and effects relevant for imaging-related simulations that are not yet fully understood, or omitted in the irradiation description. We give estimates for their contribution to the overall radiation damage. In this way we can identify unsolved issues and challenges for simulations of x-ray irradiated single molecules relevant for imaging studies. They should be addressed during further development of these simulation tools.