As one of the most widely cultivated and consumed crops, wheat is essential to global food security. However, wheat production is increasingly challenged by pests, diseases, climate change, and water scarcity, threatening yields. Traditional crop monitoring methods are labor-intensive and often ineffective for early issue detection. Hyperspectral imaging (HSI) has emerged as a non-destructive and efficient technology for remote crop health assessment. However, the high dimensionality of HSI data and limited availability of labeled samples present notable challenges. In recent years, deep learning has shown great promise in addressing these challenges due to its ability to extract and analysis complex structures. Despite advancements in applying deep learning methods to HSI data for wheat crop analysis, no comprehensive survey currently exists in this field. This review addresses this gap by summarizing benchmark datasets, tracking advancements in deep learning methods, and analyzing key applications such as variety classification, disease detection, and yield estimation. It also highlights the strengths, limitations, and future opportunities in leveraging deep learning methods for HSI-based wheat crop analysis. We have listed the current state-of-the-art papers and will continue tracking updating them in the following https://github.com/fadi-07/Awesome-Wheat-HSI-DeepLearning.