In the 90s there was lots of work on storing data in 3d holograms, by using photorefractive materials. That works by interfering a reference wave and an image wave (which contains the information in bit form for example) to create 2d maps and the multiple amps through translation. You can read out the information using a reference wave only. IBM was one of the big research labs in this space.

They achieved some impressive bit densities for the time. There were even some prototypes. However, the rapid increase of drive storage densities and the alignment issues of these systems, (together with the lack of good error correction codes I suspect), meant all this was shelved eventually.

There is now quite a bit of research on using laser writing for storage (Microsoft research is working on this for example). However largely in 2d (3d is difficult because you want 2d read outs for speed and the other layers distort your image), I think they are also thinking about spinning disc type devices, so CD 2.0.