In this Perspective, we provide a historical overview of the surface-enhanced hyper-Raman scattering (SEHRS) effect, describe its essential components, highlight the close connection between theory and experiment in several vignettes, and discuss recent analytical applications. SEHRS, the two-photon analog of surface-enhanced Raman scattering (SERS), is a spontaneous nonlinear scattering exhibited by molecules in a plasmonic field. Hyper Raman provides distinctive information on the molecular vibrations and electronic excited states of analytes. A 40-year old mystery surrounding the SEHRS spectra of R6G is used to illustrate the power of SEHRS to explore excited electronic states, revealing how non-Condon effects can influence the two-photon molecular properties. The exceptionally large enhancement factors (>1013) obtained from SEHRS enable the analysis of single molecules and molecules at very low concentrations. This high sensitivity is further augmented by an increased sensitivity to chemical effects, allowing SEHRS to probe changes in the local environment and the orientation of surface ligands. As most SEHRS experiments employ near-infrared (NIR) and short-wave infrared (SWIR) light, it also holds promise for bioimaging studies. Before concluding, we discuss future directions and challenges for the field as it moves forward.