Orchard monitoring is a vital direction of scientific research and practical application for increasing fruit production in ecological conditions. Recently, due to the development of technology and the decrease in equipment cost, the use of unmanned aerial vehicles and artificial intelligence algorithms for image acquisition and processing has achieved tremendous progress in orchards monitoring. This paper highlights the new research trends in orchard monitoring, emphasizing neural networks, unmanned aerial vehicles (UAVs), and various concrete applications. For this purpose, papers on complex topics obtained by combining keywords from the field addressed were selected and analyzed. In particular, the review considered papers on the interval 2017-2022 on the use of neural networks (as an important exponent of artificial intelligence in image processing and understanding) and UAVs in orchard monitoring and production evaluation applications. Due to their complexity, the characteristics of UAV trajectories and flights in the orchard area were highlighted. The structure and implementations of the latest neural network systems used in such applications, the databases, the software, and the obtained performances are systematically analyzed. To recommend some suggestions for researchers and end users, the use of the new concepts and their implementations were surveyed in concrete applications, such as a) identification and segmentation of orchards, trees, and crowns; b) detection of tree diseases, harmful insects, and pests; c) evaluation of fruit production, and d) evaluation of development conditions. To show the necessity of this review, in the end, a comparison is made with review articles with a related theme.