Gliomas, the most common primary brain tumors, show high heterogeneity in histological and molecular characteristics. Accurate molecular profiling, like isocitrate dehydrogenase (IDH) mutation and 1p/19q codeletion, is critical for diagnosis, treatment, and prognosis. This review evaluates MRI-based deep learning (DL) models' efficacy in predicting these biomarkers. Following PRISMA guidelines, we systematically searched major databases (PubMed, Scopus, Ovid, and Web of Science) up to February 2024, screening studies that utilized DL to predict IDH and 1p/19q codeletion status from MRI data of glioma patients. We assessed the quality and risk of bias using the radiomics quality score and QUADAS-2 tool. Our meta-analysis used a bivariate model to compute pooled sensitivity, specificity, and meta-regression to assess inter-study heterogeneity. Of the 565 articles, 57 were selected for qualitative synthesis, and 52 underwent meta-analysis. The pooled estimates showed high diagnostic performance, with validation sensitivity, specificity, and area under the curve (AUC) of 0.84 [prediction interval (PI): 0.67-0.93, I2=51.10%, p < 0.05], 0.87 [PI: 0.49-0.98, I2=82.30%, p < 0.05], and 0.89 for IDH prediction, and 0.76 [PI: 0.28-0.96, I2=77.60%, p < 0.05], 0.85 [PI: 0.49-0.97, I2=80.30%, p < 0.05], and 0.90 for 1p/19q prediction, respectively. Meta-regression analyses revealed significant heterogeneity influenced by glioma grade, data source, inclusion of non-radiomics data, MRI sequences, segmentation and feature extraction methods, and validation techniques. DL models demonstrate strong potential in predicting molecular biomarkers from MRI scans, with significant variability influenced by technical and clinical factors. Thorough external validation is necessary to increase clinical utility.