A surface wave (SW) in optics is a light wave, which is supported at an interface of two dissimilar media and propagates along the interface with its field amplitude exponentially decaying away from the boundary. Research on surface waves has been flourishing in the last few decades due to their unique properties of surface sensitivity and field localization. These features have resulted in applications in nano-guiding, sensing, light-trapping and imaging based on near-field techniques, contributing to the establishment of nanophotonics as a field of research. Up to now, a wide variety of surface waves has been investigated in numerous material and structure settings. This article reviews the recent progress and development in the physics of SWs localized at metamaterial interfaces, as well as bulk media in order to provide broader perspectives on optical surface waves in general. For each type of surface wave, we discuss the material and structural platforms. We mainly focus on experimental realizations in the visible and near-infrared wavelength ranges. We also address existing and potential application of SWs in chemical and biological sensing, and experimental excitation and characterization methods.