Over the past century, the molecular beam methods pioneered by Otto Stern have advanced our knowledge and understanding of the world enormously. Stern and his colleagues used these new techniques to measure the magnetic dipole moments of fundamental particles with results that challenged the prevailing ideas in fundamental physics at that time. Similarly, recent measurements of fundamental electric dipole moments challenge our present day theories of what lies beyond the Standard Model of particle physics. Measurements of the electron’s electric dipole moment (eEDM) rely on the techniques invented by Stern and later developed by Rabi and Ramsey. We give a brief review of this historical development and the current status of eEDM measurements. These experiments, and many others, are likely to benefit from ultracold molecules produced by laser cooling. We explain how laser cooling can be applied to molecules, review recent progress in this field, and outline some eagerly anticipated applications.