In this paper, we present a comprehensive study on deep learning methods and datasets used for solving the palmprint recognition problem. The quality of image embeddings provided by deep neural networks, pre-trained on the ImageNet dataset, are evaluated on palmprint recognition in the visible spectrum task. In our tests, we used twelve publicly available datasets obtained with different types of acquisition procedures: constrained, partially constrained and unconstrained. Sixteen convolutional neural networs (two from the VGG family, six from ResNet, three from Inception, two from MobileNet and three from DenseNet) were evaluated. We analyzed the results from the point of view of specialization potential, the difficulty of the datasets and general parameter tuning. For evaluation, EER (Equal Error Rate) was employed. We ranked the datasets and appraised the feature vectors computed by the pre-trained networks using this metric. The best results, on average, were provided by the deep neural networks from the MobileNet family. The distances used for comparing the feature vectors were Euclidean, Cityblock, cosine and correlation. The best results were obtained with the cosine family distances.