For an energy source to qualify as sustainable, it must maximize the efficiency with which it uses natural resources while minimizing the amounts of waste it produces. Currently deployed nuclear power plants however use a very limited amount of the energy contained in natural nuclear fuels such as Uranium and Thorium and produce long-lived nuclear waste that must be dealt with. Molten Salt Reactors (MSRs) are one family of advanced reactors designs with the potential for safe and sustainable energy production due to their use of a liquid molten salt fuel. This thesis aimed at reviewing MSR designs that have been proposed in the past, investigating alternative design possibilities and proposing a concept capable of disposing of existing waste in a sustainable manner. One possibility to do so is to design a reactor to run on an isobreeding closed fuel cycle while using existing actinide waste as a start-up inventory, which is the route investigated in this thesis. For this purpose, the EQL0D fuel cycle procedure was developed using the MATLAB environment and the Serpent 2 Monte Carlo neutron transport code to simulate the start-up, transition and equilibrium of MSRs. The procedure was then applied to investigate the performance at equilibrium of several candidate fuel salts and moderators in an infinite lattice and in a closed Uranium-Plutonium and Thorium-Uranium fuel cycle. The results showed that only an isobreeding closed Uranium-Thorium fuel cycle can be achieved in moderated MSRs, while both isobreeding Uranium-Plutonium and Thorium-Uranium closed fuel cycles can be sustained in fast-spectrum MSRs, which additionally show a substantial reactivity margin that enable them to dispose of poorly fissile nuclides. The transition behavior of selected fluoride- and chloride-fueled reactors was then investigated. The fluoride-fueled cores all feature a closed Thorium-Uranium fuel cycle and included two historical graphite-moderated designs (the single- and two-fluid Molten Salt Breeder Reactors) and a modern fast-spectrum design (Molten Salt Fast Reactor). The chloride-fueled cores were proposed based on the results obtained in the infinite lattice study. The results obtained indicated that the transuranic-burning capabilities of fluoride-fueled reactors are substantially limited by the low solubility of transuranic trifluorides in fluoride salt mixtures, while no such limitation was found in chloride salts. On the other hand, chloride salts necessitate substantially larger cores and inventories. Finally, the possibility of operating MSRs on two types of open cycles without fuel processing, breed-and-burn and once-through, was investigated to alleviate concerns related to the uncertainties related to the technical feasibility of molten salt fuel processing in closed fuel cycles. The results obtained show that it is possible to operate chloride-fueled MSRs in a sustainable breed-and-burn fuel cycle and also on an open cycle with appreciable burn-ups achieved.