In the last 10 years, development in robotics, computer vision, and sensor technology has provided new spectral remote sensing tools to capture unprecedented ultra-high spatial and high spectral resolution with unmanned aerial vehicles (UAVs). This development has led to a revolution in geospatial data collection in which not only few specialist data providers collect and deliver remotely sensed data, but a whole diverse community is potentially able to gather geospatial data that fit their needs. However, the diversification of sensing systems and user applications challenges the common application of good practice procedures that ensure the quality of the data. This challenge can only be met by establishing and communicating common procedures that have had demonstrated success in scientific experiments and operational demonstrations. In this review, we evaluate the state-of-the-art methods in UAV spectral remote sensing and discuss sensor technology, measurement procedures, geometric processing, and radiometric calibration based on the literature and more than a decade of experimentation. We follow the 'journey' of the reflected energy from the particle in the environment to its representation as a pixel in a 2D or 2.5D map, or 3D spectral point cloud. Additionally, we reflect on the current revolution in remote sensing, and identify trends, potential opportunities, and limitations.