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Prostate cancer is the second most frequent cancer in men worldwide after lung cancer. Its diagnosis is based on the identification of the Gleason score that evaluates the abnormality of cells in glands through the analysis of the different Gleason patterns within tissue samples. The recent advancements in computational pathology, a domain aiming at developing algorithms to automatically analyze digitized histopathology images, lead to a large variety and availability of datasets and algorithms for Gleason grading and scoring. However, there is no clear consensus on which methods are best suited for each problem in relation to the characteristics of data and labels. This paper provides a systematic comparison on nine datasets with state-of-the-art training approaches for deep neural networks (including fully-supervised learning, weakly-supervised learning, semi-supervised learning, Additive-MIL, Attention-Based MIL, Dual-Stream MIL, TransMIL and CLAM) applied to Gleason grading and scoring tasks. The nine datasets are collected from pathology institutes and openly accessible repositories. The results show that the best methods for Gleason grading and Gleason scoring tasks are fully supervised learning and CLAM, respectively, guiding researchers to the best practice to adopt depending on the task to solve and the labels that are available. • We perform a systematic comparison of 12 training approaches on Gleason grading and scoring. • 9 highly-heterogeneous datasets were used, allowing evaluating the performance and the generalization of the methods over many datasets. • Self-supervision improves performance compared to using pre-trained weights. • Full supervision shows the highest performance in patch-level classification tasks. • CLAM obtains the highest performance in image-level classification tasks. [ABSTRACT FROM AUTHOR]