Abstract: While there has been significant focus on making high-conductance molecular wires, it is equally challenging to make extremely low conductance systems. Here we present some of our efforts to find highly insulating molecules. We have found the first molecule with clear suppression of the single-molecule conductance due to what is known as σ-interference. The interference effects in this system are so significant that our calculations show that the central unit is more insulating than a vacuum gap of the same dimensions. Through an extensive investigation of a family of molecules we show that their transport properties can largely be understood by considering these otherwise complex molecules as constrained linear systems. Varying the constituent atoms between carbon, silicon, and germanium, we now know that the majority of molecules in the so-called bicyclo[2.2.2]octane class are likely to be highly insulating. Finally, we have recently discovered the factors that can be critical for the appearance of such a significant destructive interference.