What is the conductance of a single molecule? This basic and seemingly simple question has been a difficult one to answer for both experimentalists and theorists. To determine the conductance of a molecule, one must wire the molecule reliably to at least two electrodes. The conductance of the molecule thus depends not only on the intrinsic properties of the molecule, but also on the electrode materials. Furthermore, the conductance is sensitive to the atomic-level details of the molecule-electrode contact and the local environment of the molecule. Creating identical contact geometries has been a challenging experimental problem, and the lack of atomic-level structural information of the contacts makes it hard to compare calculations with measurements. Despite the difficulties, researchers have made substantial advances in recent years. This review provides an overview of the experimental advances, discusses the advantages and drawbacks of different techniques, and explores remaining issues.