> thorium

There are two different things here, one is molten fuel and the other is thorium breeding.

Molten fuel is a really big deal because you lose the pressure, so then you don't need any pressure vessels, containment, etc. If it's a slow reactor like the MSRE they ran in the 60s, you have a graphite core and hot molten salt with uranium dissolved in it. When the salt passes through the core, the graphite moderates the neutrons which causes reaction and it gets hot, when it's not in the core, it doesn't.

The other really big deal about molten fuel is that it's a liquid, so chemists can do chemistry on it, like for example extracting the waste (and just the waste) and then putting the other 95% good fuel back in to run again. PWRs retire fuel pellets when they're no longer good for reacting, which is when they're about 5% degraded.

The challenge with molten salt is it corrodes things, and that nobody can get permits to build it. There are like 4 or 5 companies trying to build them in the west and it's all just held up on permits.

Thorium is a whole other topic. The thing about thorium is that it's really really abundant, and if you bombard it with neutrons, it will transform into uranium 233. So people have the idea of surrounding the reactor with a layer of thorium to absorb the wasted neutrons and convert it whilst running the normal uranium reaction. But this is not necessary for molten salt, it's just a stretch goal. Uranium is already like $60 a pound which is basically dirt cheap for the amounts you actually need.

The MSRE did not breed thorium, but Alvin Weinberg (administrator of the MSRE and also inventor of everybody's favorite PWR) suggested that it could.