We describe our research into building integrated molecular electronics circuitry for a diverse set of functions, and with a focus on the fundamental scientific issues that surround this project. In particular, we discuss experiments aimed at understanding the function of bistable rotaxane molecular electronic switches by correlating the switching kinetics and ground state thermodynamic properties of those switches in various environments, ranging from the solution phase to a Langmuir monolayer of the switching molecules sandwiched between two electrodes. We discuss various devices, low bit-density memory circuits, and ultra-high density memory circuits that utilize the electrochemical switching characteristics of these molecules in conjunction with novel patterning methods. We also discuss interconnect schemes that are capable of bridging the micrometre to submicrometre length scales of conventional patterning approaches to the near-molecular length scales of the ultra-dense memory circuits. Finally, we discuss some of the challenges associated with fabricated ultra-dense molecular electronic integrated circuits.