[contravariant]

At this stage there's really only a couple of options. More than there used to be, but still.

When you want to stay faithful to the actual data then your options are limited, for quite a large part of the image a simple convolution is about as good as it gets, except for the edges. Basically the only problem we couldn't solve 20 years ago was excessive ringing (which is why softer scaling algorithms were preferred). You can put quite a lot of effort into getting clearer edges, especially for thin lines, but for most content you can't expect too much more sharpness than what the basic methods get you.

And then there is the generative approach where you just make stuff up. It's quite effective but a bit iffy. It's fine for entertainment but it's debatable if the result is actually a true rescale of the image (and if you average over the distribution of possible images the result is too soft again).

In theory video can do better by merging several frames of the same content.