Results of coherent diffractive imaging experiments performed with soft X-rays (1-2 keV) at the Linac Coherent Light Source are presented. Both organic and inorganic nano-sized objects were injected into the XFEL beam as an aerosol focused with an aerodynamic lens. The high intensity and femtosecond duration of X-ray pulses produced by the Linac Coherent Light Source allow structural information to be recorded by X-ray diffraction before the particle is destroyed. Images were formed by using iterative methods to phase single shot diffraction patterns. Strategies for improving the reconstruction methods have been developed. This technique opens up exciting opportunities for biological imaging, allowing structure determination without freezing, staining or crystallization.