Ultrafast two-dimensional infrared spectroscopy (2D IR) has been advanced in recent years toward measuring signals from only a monolayer of sample molecules at solid-liquid and solid-gas interfaces. A series of experimental methods has been introduced, which in the chronological order of development are 2D sum-frequency-generation (2D SFG), transmission 2D IR, and reflection 2D IR, the latter in either internal, attenuated total reflection (ATR), or external reflection configuration. The different variants of 2D vibrational spectroscopy are based on either the even-order or the odd-order nonlinear susceptibility, and all allow resolving similar molecular temporal and spectral information. In this review, we introduce the basic principles of the different methods of 2D vibrational spectroscopy at surfaces along with a balanced overview on the technological aspects as well as benefits and shortcomings. We furthermore discuss the current scope of applications for 2D vibrational surface spectroscopy, which spans an impressively broad range of samples from biological molecules to heterogeneous catalysts. The emphasis is on the ultrafast structural dynamics of molecules at interfaces, environmental interactions, and intermolecular interactions. We furthermore consider important recent technological developments of 2D vibrational surface spectroscopy, which employ (i) surface enhancement, (ii) methods for studying electrochemical interfaces, and (iii) extensions for resolving nonequilibrium processes (transient 2D IR). A detailed outlook is finally given regarding important future applications and technological developments of 2D vibrational surface spectroscopy.