Case in point, this recent restoration of Morecambe and Wise by BBC R&D: http://www.bbc.co.uk/rd/blog/2017-12-morecambe-wise-video-fi...
They laser cut the film apart, then used X-ray microtomography to scan the film and some very clever software to unwarp layers from the 3D data produced by the X-ray microtomography process. Not exactly something we could've done 5 years ago.
Please post to HN front page and re-post as updates occur!
In the case of the Morecambe and Wise recordings, this was video to film (with an additional step to try to lose information in the first conversion so that the scan lines were less visible) so the interesting technique here was simply in restoring a degraded source. Unlike scans of film negatives, there is no way a new process or technique is going to dig out information that the original low-fidelity recording system was simply unable to capture.
Now if the support is in poor conditions, perhaps the technologies mentioned in the other posts are worth considering. But if it is a tape or film stored in decent condition, it is unlikely that future techniques will add much to current ones.