Unmanned aerial vehicles (UAVs) or drones have been developed significantly over the past two decades, for a wide variety of applications such as surveillance, geographic studies, fire monitoring, security, military applications, search and rescue, agriculture, etc. In agriculture, for example, remote sensing by means of unmanned aerial vehicles has proven to be the most efficient way to monitor crops from images. Unlike remote sensing from satellite images or taken from manned aircraft, UAVs allow capturing images of high spatial and temporal resolution, thanks to their maneuverability and capability of flying at low altitude. This article presents an extensive review of the literature on crop monitoring by UAV, identifying specific applications, types of vehicles, sensors, image processing techniques, among others. A total of 50 articles related to crop monitoring applications of UAV in agriculture were reviewed. Only journal articles indexed in the Scopus database with more than 50 citations were considered. It was found that cereals are the most common crops where remote sensing has been applied so far. In addition, the most common crop remote sensing applications are related to precision agriculture, which includes the management of weeds, pests, diseases, nutrients and others. Crop phenotyping is also a common application of remote sensing, which consists of the evaluation of a crop’s physical characteristics under environmental changes, to select the plants or seeds with favorable genotype and phenotype. Besides, multirotor is the most common type of UAV used for remote sensing and RGB and multispectral cameras are mostly used as sensors for this application. Finally, there is a great opportunity for research in remote sensing related to a wide variety of crops, crop monitoring applications, vegetation indexes and photogrammetry.