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The number of objects is considered an important factor in a variety of tasks in the agricultural domain. Automated counting can improve farmers decisions regarding yield estimation, stress detection, disease prevention, and more. In recent years, deep learning has been increasingly applied to many agriculture-related applications, complementing conventional computer-vision algorithms for counting agricultural objects. This article reviews progress in the past decade and the state of the art for counting methods in agriculture, focusing on deep-learning methods. It presents an overview of counting algorithms, metrics, platforms, and sensors, a list of all publicly available datasets, and an in-depth discussion of various deep-learning methods used for counting. Finally, it discusses open challenges in object counting using deep learning and gives a glimpse into new directions and future perspectives for counting research. The review reveals a major leap forward in object counting in agriculture in the past decade, led by the penetration of deep learning methods into counting platforms.