Chest Radiograph or Chest X-ray (CXR) is a common, fast, non-invasive, relatively cheap radiological examination method in medical sciences. CXRs can aid in diagnosing many lung ailments such as Pneumonia, Tuberculosis, Pneumoconiosis, COVID-19, and lung cancer. Apart from other radiological examinations, every year, 2 billion CXRs are performed worldwide. However, the availability of the workforce to handle this amount of workload in hospitals is cumbersome, particularly in developing and low-income nations. Recent advances in AI, particularly in computer vision, have drawn attention to solving challenging medical image analysis problems. Healthcare is one of the areas where AI/ML-based assistive screening/diagnostic aid can play a crucial part in social welfare. However, it faces multiple challenges, such as small sample space, data privacy, poor quality samples, adversarial attacks and most importantly, the model interpretability for reliability on machine intelligence. This paper provides a structured review of the CXR-based analysis for different tasks, lung diseases and, in particular, the challenges faced by AI/ML-based systems for diagnosis. Further, we provide an overview of existing datasets, evaluation metrics for different[][15mm][0mm]Q5 tasks and patents issued. We also present key challenges and open problems in this research domain.