Classifying or categorizing texts is the process by which documents are classified into groups by subject, title, author, etc. This paper undertakes a systematic review of the latest research in the field of the classification of Arabic texts. Several machine learning techniques can be used for text classification, but we have focused only on the recent trend of neural network algorithms. In this paper, the concept of classifying texts and classification processes are reviewed. Deep learning techniques in classification and its type are discussed in this paper as well. Neural networks of various types, namely, RNN, CNN, FFNN, and LSTM, are identified as the subject of study. Through systematic study, 12 research papers related to the field of the classification of Arabic texts using neural networks are obtained: for each paper the methodology for each type of neural network and the accuracy ration for each type is determined. The evaluation criteria used in the algorithms of different neural network types and how they play a large role in the highly accurate classification of Arabic texts are discussed. Our results provide some findings regarding how deep learning models can be used to improve text classification research in Arabic language.