Ternary compounds based on molybdenum chalcogenide clusters Mo6X8 display a wide variety of physical properties, depending on both their composition and crystal structure. When assembled into a three-dimensional network, they form the well-known “Chevrel phase” materials MMo6X8, many of which become superconducting at low temperature. However, they may also condense into highly one-dimensional infinite-length chains with formula M2Mo6Se6. These materials either become superconducting or undergo a metal-insulator transition at low temperature, depending on the nature of the M atom. This thesis describes two powerful experimental techniques – sub-Kelvin scanning tunnelling microscopy (STM) and specific heat measurements – and their application to the study of the physical properties of various molybdenum cluster compounds. An explanation is provided for the behavioural trends seen across the M2Mo6Se6 family and a detailed analysis of the superconducting state performed for SnMo6S8 and PbMo6S8.