We present a perspective on the use of potential-dependent broadband multiplex vibrational sum-frequency generation spectroscopy (hereafter SFG) to study electrochemical systems. In SFG, a broadband mid-infrared (IR) pulse is combined with a narrowband visible pulse, generating a pulse at the sum frequency, which contains a spectrum that, due to the principles of nonlinear optics, originates solely from the electrified interface. Our SFG spectrometer can obtain one hundred or more spectra during a routine cyclic voltammetry (CV) measurement. We used SFG to study a model for a Li-ion battery anode and a low-overpotential CO2 reduction reactor based on a room-temperature ionic liquid (RTIL). SFG spectra from these complex systems were difficult to interpret, in part due to the organic electrolytes that have a forest of infrared vibrational transitions. Here we discuss a rubric for experimental measurement and interpretation with such systems. We describe the electrified interface, or double layer, as consisting of the electrode surface, a region of adsorbed molecules and an outer diffuse electric double layer. We combined resonant SFG, where the IR pulses were tuned to vibrational transitions of adsorbates, with nonresonant SFG where the IR pulses were tuned away from all vibrational transitions. The former provides information about chemistry on the electrode surface and the latter about the potential-dependent response of the double layer. We show how this rubric can be used to understand solid-electrolyte interphase formation on a model for the Li-ion electrode, and how low-overpotential CO2 reduction on Ag is controlled by potential-driven structural transitions of the RTIL electrolyte.