Towards the need for sustainable development, remote sensing (RS) techniques in the Visible-Near Infrared–Shortwave Infrared (VNIR–SWIR, 400–2500 nm) region could assist in a more direct, cost-effective and rapid manner to estimate important indicators for soil monitoring purposes. Soil reflectance spectroscopy has been applied in various domains apart from laboratory conditions, e.g., sensors mounted on satellites, aircrafts and Unmanned Aerial Systems. The aim of this review is to illustrate the research made for soil organic carbon estimation, with the use of RS techniques, reporting the methodology and results of each study. It also aims to provide a comprehensive introduction in soil spectroscopy for those who are less conversant with the subject. In total, 28 journal articles were selected and further analysed. It was observed that prediction accuracy reduces from Unmanned Aerial Systems (UASs) to satellite platforms, though advances in machine learning techniques could further assist in the generation of better calibration models. There are some challenges concerning atmospheric, radiometric and geometric corrections, vegetation cover, soil moisture and roughness that still need to be addressed. The advantages and disadvantages of each approach are highlighted and future considerations are also discussed at the end.