Micro- or nanostructured surfaces can provide a significant slip to a fluid flowing over the surface, making them attractive for the development of functional coatings. This slip is due to a second fluid being entrapped in the indentations of the structured surface, like air for superhydrophobic surfaces or oil for so-called lubricant-infused surfaces (SLIPS). This talk addresses the flow phenomena close to such surfaces. An analytical model is presented that describes the flow field as well as the effective slip length for flow over a surface with rectangular grooves. The model captures arbitrary geometries of the grooves as well as a Newtonian fluid of arbitrary viscosity being entrapped in the grooves. It can for example be employed as a guideline to design efficient surface coatings for drag reduction. Additionally, corresponding experiments on the flow field and local slip length close to a superhydrophobic surface are presented. While the global behavior of flow past superhydrophobic surfaces has been widely investigated, the local flow phenomena have not yet been observed experimentally. Using fluorescence correlation spectroscopy, we performed detailed measurements of the flow in close vicinity to the surface. We explain the distribution of the local slip length by the local hydrodynamics within the air layer and at the air-water interface and show that slippage can be significantly influenced by the presence of surface-active substances adhering to the air-water interface.