Lensless microscopy, which is also called coherent diffractive imaging (CDI), is a novel and revolutionary approach to imaging. Compared to lens-based microscopy i.e. optical, fluorescence or electron microscopy, lensless microscopy does not need to rely on lenses to obtain the image of the sample. Instead of this, lensless microscopy relies on coherence of the illumination and on computational postprocessing of the measured data. This allows CDI methods huge flexibility in imaging setups compared to the lens-based microscopy. The family of CDI methods has been growing rapidly over the last years. The first simple application in the X-ray regime for imaging of aperiodic (non-crystalline) samples was done by Janwei Miao et al. In this experiment no optics were used around the sample and a single diffraction pattern was used to reconstruct the image. The current state of the art CDI applications collect thousands of images that are subsequently processed together by an appropriate method to create up to gigapixel resolution images. CDI generally has several advantages compared to the ordinary lens-based imaging: firstly the image quality is not limited by the quality of lenses. Instead of an objective lens, a numerical iterative algorithm is used. The maximum resolution of CDI is, similarly to lens-based systems, limited by the highest spatial frequency collected by the imaging system. The advantage of CDI is the possibility of either avoiding the imaging lenses or including their limited quality into the reconstruction process. However, the main advantage of the CDI methods is to recover both phase and amplitude of the exit-wave field behind the sample. This allows to obtain much higher contrast for phase objects that would have otherwise low contrast in bright field microscopy. The ability of the phase and amplitude recovery without limitation of lenses makes CDI a powerful method with a broad range of applications in nanoscience, material science and biology.