Multi-class tissue classification from histological images is a complex challenge. The gold standard still relies on manual assessment by a trained pathologist, but it is a time-expensive task with issues about intra- and inter-operator variability. The rise of computational models in Digital Pathology has the potential to revolutionize the field. Historically, image classifiers relied on handcrafted feature extraction, combined with statistical classifiers, as Support Vector Machines (SVMs) or Artificial Neural Networks (ANNs). In recent years, there has been a tremendous growth in Deep Learning (DL), for all the image recognition tasks, including, of course, those concerning medical images. Thanks to DL, it is now possible to also learn the process of capturing the most relevant features from the image, easing the design of specialized classification algorithms and improving the performance. An important problem of DL is that it requires tons of training data, which is not easy to obtain in medical domain, since images have to be annotated by expert physicians. In this work, we extensively compared three classes of approaches for the multi-class tissue classification task: (1) extraction of handcrafted features with the adoption of a statistical classifier; (2) extraction of deep features using the transfer learning paradigm, then exploiting SVM or ANN classifiers; (3) fine-tuning of deep classifiers. After a cross-validation on a publicly available dataset, we validated our results on two independent test sets, obtaining an accuracy of 97% and of 77%, respectively. The second test set has been provided by the Pathology Department of IRCCS Istituto Tumori Giovanni Paolo II and has been made publicly available (http://doi.org/10.5281/zenodo.4785131 ).