Speech recognition is a technology that enables humans and machines to communicate by converting spoken words into text. Hindi is spoken extensively in various regions of India and is also used in various global locations. This paper comprehensively reviews deep learning methods for Hindi speech recognition. Challenges associated with speech recognition are presented. Various speech recognition tools and databases are discussed. A comparative analysis of different deep learning-based Hindi speech recognition systems is presented. Other performance parameters are studied. The findings demonstrate that the convolution neural network (CNN) is mainly used for speech recognition. The main contribution of this research work is providing a comprehensive background and technical details of the deep learning-based Hindi speech recognition system. This is achieved by presenting details of appropriate models, tools, and features that can be utilized to improve the system. The work can be extended by going deeper into deep learning-based systems.