Similar to a child demonstrating how he can ride a bicycle without using his hands, now we have scientists taking pictures without a lens.
Upon reflection, it was a predictable next step. First we had the major advance of refocusing out-of-focus images by, in essence, building a correction lens, all in software. This is what allowed NASA (the USA space agency) to correct some of the Hubble Space Telescope images after it was put into orbit with an out-of-focus optical chain.
But it one can simulate a lens well enough to correct an image, even if imperfectly, why not replace the real lens with a simulated one and focus the unfocused image received by the (lens-less) sensor? That is what the team at Argonne National Laboratory (Illinois, USA) is working on. Of course, simulations are rarely, if ever, as good as the real thing in all aspects, but if for their particular problem (X-ray imaging) the simulated lens is better than their real one, then they will have improved the imaging system and advanced the state of the art yet again.