Horticultural enterprises are becoming more sophisticated as the range of the crops they target expands. Requirements for enhanced efficiency and productivity have driven the demand for automating on-field operations. However, various problems remain yet to be solved for their reliable, safe deployment in real-world scenarios. This paper examines major research trends and current challenges in horticultural robotics. Specifically, our work focuses on sensing and perception in the three main horticultural procedures: pollination, yield estimation, and harvesting. For each task, we expose major issues arising from the unstructured, cluttered, and rugged nature of field environments, including variable lighting conditions and difficulties in fruit-specific detection, and highlight promising contemporary studies.