Artificial neural networks (ANNs) ability to learn, correct errors, and transform a large amount of raw data into beneficial medical decisions for treatment and care has increased in popularity for enhanced patient safety and quality of care. Therefore, this paper reviews the critical role of ANNs in providing valuable insights for patients’ healthcare decisions and efficient disease diagnosis. We study different types of ANNs in the existing literature that advance ANNs’ adaptation for complex applications. Specifically, we investigate ANNs’ advances for predicting viral, cancer, skin, and COVID-19 diseases. Furthermore, we propose a deep convolutional neural network (CNN) model called ConXNet, based on chest radiography images, to improve the detection accuracy of COVID-19 disease. ConXNet is trained and tested using a chest radiography image dataset obtained from Kaggle, achieving more than 97% accuracy and 98% precision, which is better than other existing state-of-the-art models, such as DeTraC, U-Net, COVID MTNet, and COVID-Net, having 93.1%, 94.10%, 84.76%, and 90% accuracy and 94%, 95%, 85%, and 92% precision, respectively. The results show that the ConXNet model performed significantly well for a relatively large dataset compared with the aforementioned models. Moreover, the ConXNet model reduces the time complexity by using dropout layers and batch normalization techniques. Finally, we highlight future research directions and challenges, such as the complexity of the algorithms, insufficient available data, privacy and security, and integration of biosensing with ANNs. These research directions require considerable attention for improving the scope of ANNs for medical diagnostic and treatment applications.