The molten salt reactor (MSR) is one of the leading advanced nuclear reactor candidates to replace current nuclear reactor technologies in the U.S. Besides having more economical and reliable designs, MSRs are amenable to a closed fuel cycle, in which electrochemical reprocessing can be performed to recycle the used nuclear fuel. This review intends to provide information about potential waste forms for metal and salt waste streams from these salt-based nuclear processes. Metal waste streams arise from reactor components and structural materials. Salt waste streams are generated during reactor operations as fission products build up in salt-fuelled systems. Waste forms that have the highest waste loading and/or have shown the most commercial promise are discussed with an emphasis on the current state of efforts to understand the synthesis and chemical durability of metal and ceramic waste forms.