Handwriting, drawing, or patterns can be used to detect cognitive and personality disorders. Automating psychological tests can help to detect mental disorders early and prevent it from getting worse and with irreversible consequences. Automation of psychological drawing tests requires reviewing datasets of psychological drawing tests, reviewing image classification algorithms as an essential step, and finally reviewing the scoring of tests according to the standards. In this study, the recent researches in the field of datasets of drawing and handwritten tests, various methods of classification of drawing tests, scoring techniques to the tests and challenges ahead have been thoroughly investigated. So far, no such comprehensive research has been conducted on datasets, classification algorithms, and automatic detection in psychological drawing tests. Also, a comprehensive comparison of how datasets are collected, drawing test classification methods, test comparison techniques with the standards, advantages, and disadvantages of each method is presented. Challenges in the process of automatic diagnosis in psychological drawing tests are also discussed. This study aims to identify fast, accurate methods with low processing load and high reliability. In this study, by comparing the presented methods, it is concluded that in classifying images and detecting mental disorders, neural network algorithms have higher accuracy than machine learning algorithms, but are slower.