Deep Neural Networks (DNNs) learn representation from data with an impressive capability, and brought important breakthroughs for processing images, time-series, natural language, audio, video, and many others. In the remote sensing field, surveys and literature revisions specifically involving DNNs algorithms applications have been conducted in an attempt to summarize the amount of information produced in its subfields. Recently, Unmanned Aerial Vehicles (UAV) based applications have dominated aerial sensing research. However, a literature revision that combines both deep learning and UAV remote sensing thematics has not yet been conducted. The motivation for our work was to present a comprehensive review of the fundamentals of Deep Learning (DL) applied in UAV-based imagery. We focused mainly on describing classification and regression techniques used in recent applications with UAV-acquired data. For that, a total of 232 papers published in international scientific journal databases was examined. We gathered the published material and evaluated their characteristics regarding application, sensor, and technique used. We relate how DL presents promising results and has the potential for processing tasks associated with UAV-based image data. Lastly, we project future perspectives, commentating on prominent DL paths to be explored in the UAV remote sensing field. Our revision consists of a friendly-approach to introduce, commentate, and summarize the state-of-the-art in UAV-based image applications with DNNs algorithms in diverse subfields of remote sensing, grouping it in the environmental, urban, and agricultural contexts.