Chest diseases are very serious health problems in the life of people. These diseases include chronic obstructive pulmonary disease, pneumonia, asthma, tuberculosis, and lung diseases. The timely diagnosis of chest diseases is very important. Many methods have been developed for this purpose. In this paper, we demonstrate the feasibility of classifying the chest pathologies in chest X-rays using conventional and deep learning approaches. In the paper, convolutional neural networks (CNNs) are presented for the diagnosis of chest diseases. The architecture of CNN and its design principle are presented. For comparative purpose, backpropagation neural networks (BPNNs) with supervised learning, competitive neural networks (CpNNs) with unsupervised learning are also constructed for diagnosis chest diseases. All the considered networks CNN, BPNN, and CpNN are trained and tested on the same chest X-ray database, and the performance of each network is discussed. Comparative results in terms of accuracy, error rate, and training time between the networks are presented.