Understanding charge transport of single molecules or a small collection of molecules sandwiched between electrodes is of fundamental importance for molecular electronics. This requires the fabrication of reliable devices, which depend on several factors including the testbed architectures used, the molecule number and defect density being tested, and the nature of the molecule-electrode interface. On the basis of significant progresses achieved in both experiments and theory over the past decade, in this tutorial review, we focus on new insights into the influence of the nature of the molecule-electrode interface, the most critical issue hindering the development of reliable devices, on the conducting properties of molecules. We summarize the strategies developed for controlling the interfacial properties and how the coupling strength between the molecules and the electrodes modulates the device properties. These analyses should be valuable for deeply understanding the relationship between the contact interface and the charge transport mechanism, which is of crucial importance for the development of molecular electronics, organic electronics, nanoelectronics, and other interface-related optoelectronic devices.