There was a lot of interest in flying wings for a long time. The Hortens discovered they had a problem with loss of lift in the centre section of theirs - so they extended the wing in the centre to give it that 'bat-plane' shape. When flown the test pilots (apparently) said it flew really nicely. After the war neither the Brits or the Yanks seriously tried extending the centre section's of their flying wings and testing the aerodynamics the way the Hortens did. I don't know why.
However the 'bat-plane' (Horten IX or Ho-229) internally was a mess. If it they had been given better resources it might have been a very different story. I fail to understand why the allies didn't try to build such a wing using the aerodynamic experience of the Hortens after the war. The original plane itself wasn't adequate to take further - but a new plane may have looked the same/similar.
Even if it had reached service though, the flying wing concept has problems when reaching trans-sonic speeds (excessive buffeting). I'm not sure if that applies to the Horten design - I don't believe anyone has tried - but it probably does.