Precision farming has become a hot research topic in recent years due to the advancement of sensing technologies, increased computer performance, and advanced deep learning algorithms. As a result, several outstanding studies on deep learning applications to high-throughput phenotyping of wheat, one of the most demanding cereal crops on the planet, have been published. This paper aims to conduct a survey of publications that have used deep learning techniques to address various challenges in wheat production. To accomplish this, we propose an ontology-based knowledge management system that is specifically designed to highlight the publications' objectives, preprocessing algorithms, deep learning models, frameworks, datasets, and results. The presented ontology is intended to serve as a robust tool for future research in wheat high-throughput phenotyping. Additionally, we compare the performance of deep learning algorithms to that of long-established methods in this field. Compared to traditional machine learning techniques, this study demonstrates that deep learning algorithms provide a more robust, accurate, and cost-effective way of measuring wheat traits.