In the last years, there has been a real growth of interest in the use of high-temperature molten salt fluorides as coolants and fuel salts in nuclear power systems. For all molten salt reactor (MSR) concepts, material selection is a very important issue. This paper summarizes results of recent work done within the ISTC#1606 project and the present state of knowledge about container materials for MSRs. The central focus is the compatibility of Ni-based alloys with the molten Li,Na,Be/F salt system as applied to the primary circuit of the MOlten Salt Actinide Recycler & Transmuter (MOSART) fueled with different compositions of actinide trifluorides from light water reactor spent fuel without U-Th support. Results from recent studies with a Li,Na,Be/F thermal convection loop at temperatures up to 700°C are presented. Material specimens of three modified Hastelloy N alloys, particularly HN80M-VI with 1% of Nb, HN80MTY with 1% of Al, and MONICR with 2% of Fe, were used for our study in corrosion facilities. Methods to purify the molten salt composition and to improve Ni-based container alloy compatibility by maintaining the salt at a low redox potential are discussed. The effect on materials compatibility of adding plutonium trifluoride and tellurium to the Li,Na,Be/F solvent system is also considered. Last, testing of advanced Ni-based alloys with various compositions to enhance first of all its resistance to tellurium intergranular cracking should be continued in thermal convection loops with a long exposure time for the MOSART fuel salts as well as the novel nonmoderated thorium sustainable MSR concept in the framework of the new ISTC#3749 project.