There are plants of various ages beacause it was an area of active research in late 1900s, and a handful of industrial scale plants that are operating. But it's not generally happening or growing. For most used fuel there is no plan, or going to be buried underground.

All the ones shown in green are still operating.

It hasn't been in high demand because virgin uranium is still cheap. That won't be the case forever, and the used fuel pellets will be waiting when that occurs.

The UK reprocessing plants at least are environmental disasters with a history of large-scale radioactive discharges into the surrounding environment. (Russia's were even worse, apparently.) They also lost their foreign customers for falsifying data on fuel shipments. They're due to shut down altogether in the next few years as their existing contracts come to an end. Unfortunately, the Sellafield site is probably impossible to decommission safely due to massive contamination and poorly-designed containments with no documentation of the contents.

Also, most of the big reprocessing plants out there were originally constructed as part of nuclear weapons programs, including the UK, US, French and Russian ones. They're just not economically viable otherwise.

The list has 6 active ones with > 100t/year capacity, more are being decommissioned than built.

Uranium is going to stay sufficiently cheap to our best current knowledge (we'll probably keep find new deposits, or it can be extracted from seawater for much cheaper than reprocessing spent fuel)