The main MSR concept is to have the fuel dissolved in the coolant as fuel salt, and ultimately to reprocess that online.
Thorium, uranium, and plutonium all form suitable fluoride salts that readily dissolve in the LiF-BeF2 (FLiBe) mixture, and thorium and uranium can be easily separated from one another in fluoride form.
Batch reprocessing is likely in the short term, and fuel life is quoted at 4-7 years, with high burn-up. Intermediate designs and the AHTR have fuel particles in solid graphite and have less potential for thorium use.