Biomass is an important indicator for evaluating crops. The rapid, accurate and nondestructive monitoring of biomass is the key to smart agriculture and precision agriculture. Traditional detection methods are based on destructive measurements. Although satellite remote sensing, manned airborne equipment, and vehicle-mounted equipment can nondestructively collect measurements, they are limited by low accuracy, poor flexibility, and high cost. As nondestructive remote sensing equipment with high precision, high flexibility, and low-cost, unmanned aerial systems (UAS) have been widely used to monitor crop biomass. In this review, UAS platforms and sensors, biomass indices, and data analysis methods are presented. The improvements of UAS in monitoring crop biomass in recent years are introduced, and multisensor fusion, multi-index fusion, the consideration of features not directly related to monitoring biomass, the adoption of advanced algorithms and the use of low-cost sensors are reviewed to highlight the potential for monitoring crop biomass with UAS. Considering the progress made to solve this type of problem, we also suggest some directions for future research. Furthermore, it is expected that the challenge of UAS promotion will be overcome in the future, which is conducive to the realization of smart agriculture and precision agriculture.