Melanoma is the type of skin cancer with the highest levels of mortality, and it is more dangerous because it can spread to other parts of the body if not caught and treated early. Melanoma diagnosis is a complex task, even for expert dermatologists, mainly due to the great variety of morphologies in moles of patients. Accordingly, the automatic diagnosis of melanoma is a task that poses the challenge of developing efficient computational methods that ease the diagnostic and, therefore, aid dermatologists in decision-making. In this work, an extensive analysis was conducted, aiming at assessing and illustrating the effectiveness of convolutional neural networks in coping with this complex task. To achieve this objective, twelve well-known convolutional network models were evaluated on eleven public image datasets. The experimental study comprised five phases, where first it was analyzed the sensitivity of the models regarding the optimization algorithm used for their training, and then it was analyzed the impact in performance when using different techniques such as cost-sensitive learning, data augmentation and transfer learning. The conducted study confirmed the usefulness, effectiveness and robustness of different convolutional architectures in solving melanoma diagnosis problem. Also, important guidelines to researchers working on this area were provided, easing the selection of both the proper convolutional model and technique according the characteristics of data.Copyright © 2020 Elsevier B.V. All rights reserved.