Deep learning (DL) is poised to redefine the way medical images are processed and analyzed. Convolutional neural networks (CNNs), a specific type of DL architecture, are exceptional for high-throughput processing, allowing for the effective extraction of relevant diagnostic patterns from large volumes of complex visual data. This technology has garnered substantial interest in the field of neuro-oncology as a promising tool to enhance medical imaging throughput and analysis. A multitude of methods harnessing MRI-based CNNs have been proposed for brain tumor segmentation, classification, and prognosis prediction. They are often applied to gliomas, the most common primary brain cancer, to classify subtypes with the goal of guiding therapy decisions. Additionally, the difficulty of repeating brain biopsies to evaluate treatment response in the setting of often confusing imaging findings provides a unique niche for CNNs to help distinguish the treatment response to gliomas. For example, glioblastoma, the most aggressive type of brain cancer, can grow due to poor treatment response, can appear to grow acutely due to treatment-related inflammation as the tumor dies (pseudo-progression), or falsely appear to be regrowing after treatment as a result of brain damage from radiation (radiation necrosis). CNNs are being applied to separate this diagnostic dilemma. This review provides a detailed synthesis of recent DL methods and applications for intratumor segmentation, glioma classification, and prognosis prediction. Furthermore, this review discusses the future direction of MRI-based CNN in the field of neuro-oncology and challenges in model interpretability, data availability, and computation efficiency.