Brain tumors remain among the most aggressive neurological disorders, where diagnostic delays can critically impact survival outcomes. Accurate detection relies heavily on neuroimaging, with magnetic resonance imaging (MRI) offering high soft-tissue contrast and computed tomography (CT) providing superior detection of calcifications, hemorrhage, and bone involvement. This survey systematically examines numerous studies published between 2022 and 2025 on MRI-based, CT-based, and multimodal fusion approaches for brain tumor classification. The analysis spans methodological advances in convolutional neural networks (CNNs), attention mechanisms, transformer-based architectures, and quantum or quantum-inspired designs, with emphasis on lightweight, interpretable models suitable for clinical deployment. Comparative study highlights that integrating CT and MRI-via early, late, or attention-driven fusion-consistently improves diagnostic accuracy and robustness over singlemodality approaches. However, current fusion strategies often face trade-offs between computational efficiency and interpretability. The synthesis identifies a pressing need for low-latency, hardware-friendly fusion architectures that retain high performance and generalizability, thereby supporting wider adoption in hospital settings and improving timely clinical decision-making.  Kulcsszavak: brain-tumor classification, MRI-CT data fusion, multimodal fusion, medical imaging, quantum-inspired, CT-MRI-based classification