So far, we've been talking about monoscopic media—a 360-degree photo or video shot with a single lens point of view, albeit from all directions. When viewed in VR, yes, there are left and right eyes, but this is a stereo view of the same flat image that was projected onto a sphere. It doesn't provide any real parallax or illusion of depth through occlusion. You can rotate your head, but you should not move its position from the center of the sphere. Otherwise, the immersive illusion may be broken.
What about true 360-degree stereo? What if each eye has its own photo sphere offset from the other eye's position? Stereoscopic 360-degree recording and playback is a very difficult problem.
To capture non-stereo 360-degree media, you can use a rig such as GoPro Kolor, pictured in the following image on the left. It records all six directions at once with six separate GoPro cameras. The synchronized videos are then stitched together with special, advanced imaging software...