This paper reviews the most recent literature on experiments with different Machine Learning, Deep Learning and Natural Language Processing techniques applied to predict judicial and administrative decisions. Among the most outstanding findings, we have that the most used data mining techniques are Support Vector Machine (SVM), K Nearest Neighbours (K-NN) and Random Forest (RF), and in terms of the most used deep learning techniques, we found Long-Term Memory (LSTM) and transformers such as BERT. An important finding in the papers reviewed was that the use of machine learning techniques has prevailed over those of deep learning. Regarding the place of origin of the research carried out, we found that 64% of the works belong to studies carried out in English-speaking countries, 8% in Portuguese and 28% in other languages (such as German, Chinese, Turkish, Spanish, etc.). Very few works of this type have been carried out in Spanish-speaking countries. The classification criteria of the works have been based, on the one hand, on the identification of the classifiers used to predict situations (or events with legal interference) or judicial decisions and, on the other hand, on the application of classifiers to the phenomena regulated by the different branches of law: criminal, constitutional, human rights, administrative, intellectual property, family law, tax law and others. The corpus size analyzed in the reviewed works reached 100,000 documents in 2020. Finally, another important finding lies in the accuracy of these predictive techniques, reaching predictions of over 60% in different branches of law.