When dealing with ultra-wide fields of view, your typical lens will start to curve the straight lines: barrel distortion, or even fisheye distortion. Rectilinear lenses remedy this by having an opposite distortion of an equal amount going the other way (I don't know the exact science), but a consequence of that is this bizarres stretching at the edges even if the lines are straight. Spheres become skewed ellipses etc. This look ended up being adopted by the likes of Gilliam and Kubrick.

You can recreate this look by following the steps I put there, although I think it'd only work for static shots. (Refer to this post to see how that can be done.) Use either Photoshop's lens corrector tool, or Optics Compensation in After Effects.