With FaSS-MVS, we present a fast, surface-aware semi-global optimization approach for multi-view stereo that allows for rapid depth and normal map estimation from monocular aerial video data captured by *UAV. The data estimated by FaSS-MVS, in turn, facilitate online 3D mapping, meaning that a 3D map of the scene is immediately and incrementally generated as the image data are acquired or being received. FaSS-MVS is composed of a hierarchical processing scheme in which depth and normal data, as well as corresponding confidence scores, are estimated in a coarse-to-fine manner, allowing efficient processing of large scene depths, such as those inherent in oblique images acquired by *UAV flying at low altitudes. The actual depth estimation uses a plane-sweep algorithm for dense multi-image matching to produce depth hypotheses from which the actual depth map is extracted by means of a surface-aware semi-global optimization, reducing the fronto-parallel bias of Semi-Global Matching (SGM). Given the estimated depth map, the pixel-wise surface normal information is then computed by reprojecting the depth map into a point cloud and computing the normal vectors within a confined local neighborhood. In a thorough quantitative and ablative study, we show that the accuracy of the 3D information computed by FaSS-MVS is close to that of state-of-the-art offline multi-view stereo approaches, with the error not even an order of magnitude higher than that of COLMAP. At the same time, however, the average runtime of FaSS-MVS for estimating a single depth and normal map is less than 14 % of that of COLMAP, allowing us to perform online and incremental processing of full HD images at 1–2 Hz.