Significant advances in the automated glaucoma detection techniques have been made through the employment of the Machine Learning (ML) and Deep Learning (DL) methods, an overview of which will be provided in this paper. What sets the current literature review apart is its exclusive focus on the aforementioned techniques for glaucoma detection using the Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) guidelines for filtering the selected papers. To achieve this, an advanced search was conducted in the Scopus database, specifically looking for research papers published in 2023, with the keywords "glaucoma detection", "machine learning", and "deep learning". Among the multiple found papers, the ones focusing on ML and DL techniques were selected. The best performance metrics obtained using ML recorded in the reviewed papers, were for the SVM, which achieved accuracies of 98.31%, 98.61%, 96.43%, 96.67%, 95.24%, and 98.60% in the ACRIMA, REFUGE, RIM-ONE, ORIGA-light, DRISHTI-GS, and sjchoi86-HRF databases, respectively, employing the REFUGE-trained model, while when deploying the ACRIMA-trained model, it attained accuracies of 98.92%, 99.06%, 98.27%, 97.10%, 96.97%, and 96.36%, in the same databases, respectively. The best performance metrics obtained utilizing DL recorded in the reviewed papers, were for the lightweight CNN, with an accuracy of 99.67% in the Diabetic Retinopathy (DR) and 96.5% in the Glaucoma (GL) databases. In the context of non-healthy screening, CNN achieved an accuracy of 99.03% when distinguishing between GL and DR cases. Finally, the best performance metrics were obtained using ensemble learning methods, which achieved an accuracy of 100%, specificity of 100%, and sensitivity of 100%. The current review offers valuable insights for clinicians and summarizes the recent techniques used by the ML and DL for glaucoma detection, including algorithms, databases, and evaluation criteria.