<p>Speech recognition technologies have emerged as a standalone field of human-computer interaction. Speech, as an intrinsic human capacity, makes effortless, hands-free interaction with computers through Speech Signal Processing (SSP) possible. The area of SSP continues to evolve with the extensive use of deep learning techniques. The present work analyzes various applications of deep learning in SSP, describing the complex nature of this intersection. The work investigates various areas under the deep learning framework associated with modern-day speech technology in Human-Computer Interaction (HCI), such as automated speech recognition, speaker identification, emotion identification, and natural language processing. The work presents different methods, including convolutional neural networks, hybrid models, and recurrent neural networks, to demonstrate how deep learning can handle intricate forms of speech signal structure. The area continues to grapple with challenges of data scarcity, domain adaptation, and interpretability of models. The work outlines such challenges regarding existing limitations and avenues for future work.</p>