Emerging technologies such as Internet of Things (IoT) can provide significant potential in Smart Farming and Precision Agriculture applications, enabling the acquisition of real-time environmental data. IoT devices such as Unmanned Aerial Vehicles (UAVs) can be exploited in a variety of applications related to crops management, by capturing high spatial and temporal resolution images. These technologies are expected to revolutionize agriculture, enabling decision-making in days instead of weeks, promising significant reduction in cost and increase in the yield. Such decisions enable the effective application of farm inputs, supporting the four pillars of precision agriculture, i.e., apply the right practice, at the right place, at the right time and with the right quantity. However, the actual proliferation and exploitation of UAVs in Smart Farming has not been as robust as expected mainly due to the challenges confronted when selecting and deploying the relevant technologies, including the data acquisition and image processing methods. The main problem is that still there is no standardized workflow for the use of UAVs in such applications, as it is a relatively new area. In this article, we review the most recent applications of UAVs for Precision Agriculture. We discuss the most common applications, the types of UAVs exploited and then we focus on the data acquisition methods and technologies, appointing the benefits and drawbacks of each one. We also point out the most popular processing methods of aerial imagery and discuss the outcomes of each method and the potential applications of each one in the farming operations.