Malaria is a globally widespread disease caused by parasitic protozoa transmitted to humans by infected female mosquitoes of Anopheles. It is caused in humans only by the parasite Plasmodium, further classified into four different species. Identifying malaria parasites is possible by analysing digital microscopic blood smears, which is tedious, time-consuming and error prone. So, automation of the process has assumed great importance as it helps the laborious manual process of review and diagnosis. This work focuses on deep learning-based models, by comparing off-the-shelf architectures for classifying healthy and parasite-affected cells, by investigating the four-class classification on the Plasmodium falciparum stages of life and, finally, by evaluating the robustness of the models with cross-dataset experiments on two different datasets. The main contributions to the research in this field can be resumed as follows: (i) comparing off-the-shelf architectures in the task of classifying healthy and parasite-affected cells, (ii) investigating the four-class classification on the P. falciparum stages of life and (iii) evaluating the robustness of the models with cross-dataset experiments. Eleven well-known convolutional neural networks on two public datasets have been exploited. The results show that the networks have great accuracy in binary classification, even though they lack few samples per class. Moreover, the cross-dataset experiments exhibit the need for some further regulations. In particular, ResNet-18 achieved up to 97.68% accuracy in the binary classification, while DenseNet-201 reached 99.40% accuracy on the multiclass classification. The cross-dataset experiments exhibit the limitations of deep learning approaches in such a scenario, even though combining the two datasets permitted DenseNet-201 to reach 97.45% accuracy. Naturally, this needs further investigation to improve the robustness. In general, DenseNet-201 seems to offer the most stable and robust performance, offering as a crucial candidate to further developments and modifications. Moreover, the mobile-oriented architectures showed promising and satisfactory performance in the classification of malaria parasites. The obtained results enable extensive improvements, specifically oriented to the application of object detectors for type and stage of life recognition, even in mobile environments.