Building an electronic device using individual molecules is one of the ultimate goals in nanotechnology. To achieve this it will be necessary to measure, control and understand electron transport through molecules attached to electrodes. Substantial progress has been made over the past decade and we present here an overview of some of the recent advances. Topics covered include molecular wires, two-terminal switches and diodes, three-terminal transistor-like devices and hybrid devices that use various different signals (light, magnetic fields, and chemical and mechanical signals) to control electron transport in molecules. We also discuss further issues, including molecule-electrode contacts, local heating- and current-induced instabilities, stochastic fluctuations and the development of characterization tools.