Chest X-rays are one of the most widely used diagnostic tools in medical imaging, offering critical insights into pulmonary, cardiovascular, and thoracic conditions. The advent of deep learning has significantly enhanced the ability to analyze chest X-rays, enabling accurate and automated detection, classification, and interpretation of a wide range of pathologies. This survey provides a comprehensive overview of state-of-the-art deep learning methods applied to chest X-ray analysis. It categorizes existing approaches based on their primary tasks, including disease classification, localization, segmentation, and radiology report generation, highlighting their strengths, limitations, and clinical applicability. Key challenges, such as data scarcity, variability across imaging systems, lack of interpretability, and integration into clinical workflows, are discussed in detail. The survey also explores promising directions for future research, including self-supervised learning, federated learning, multimodal data integration, and the development of explainable and robust AI systems. By synthesizing recent advancements and identifying critical gaps, this work aims to guide researchers and practitioners toward the development of clinically impactful solutions. The findings underscore the transformative potential of deep learning in chest X-ray analysis while emphasizing the need for multidisciplinary collaboration to address existing barriers and advance the field.