Using Unmanned Aerial Vehicles (UAVs) combined with various sensors brings the benefits associated with fast, automatic, and contactless spatial data collection with high resolution and accuracy. The most frequent application is the possibility of effectively creating spatial models based on photogrammetric and lidar data. This review analyzes the current possibilities of UAVs. It provides an overview of the current state of the art and research on selected parameters regarding their history and development, classification, regulation, and application in surveying with creating spatial models. Classification and regulation are based on national sources. The importance and usability of this review are also carried out by analyzing the UAV application with selected photogrammetric and lidar sensors. The study explores and discusses results achieved by many authors in recent years, synthesizing essential facts. By analyzing the network of co-occurring High-Frequency Words, in addition, we visualized the importance of the primary keyword UAV in the context of other keywords in the literary sources processed.