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Graphical abstract Highlights • Multifunctional molecular conductors of BEDT-TTF with tris(oxalato)metallate. • 2017 discovery of molecular superconductor β″-(BEDT-TTF) 2 [(H 2 O)(NH 4) 2 M(C 2 O 4) 3 ]·18-crown-6. • Kosterlitz-Thouless transition in 2D superconductor. • Chiral induction in molecular semiconductors. • Combination of ferromagnetism and metallic behaviour. Abstract This review presents the synthesis, crystal structures and conducting properties of BEDT-TTF radical-cation salts with the tris(oxalato)metallate anion [BEDT-TTF = bis(ethylenedithio)tetrathiafulvalene]. This series has received much attention owing to the wide variety of conducting properties that have been observed. As well as including numerous metals, semiconductors and insulators, there are over twenty superconductors in this series. The series also includes several examples of multifunctionality where it has been possible to combine together particular physical properties in the same lattice such as electrical conductivity with magnetism, chirality or proton conductivity. This review presents an overview of the flexibility of the coordination chemistry of the oxalate ligand and the variety of packing arrangements of the tris(oxalato)metallate complexes in the insulating layers of these radical-cation salts. [ABSTRACT FROM AUTHOR]