Accurate compensation of brain deformation is critical for reliable image-guided neurosurgery. Surgical manipulation and tumor resection induce tissue motion, causing preoperative planning images to become misaligned with the intraoperative anatomy. In this review, we examine methods developed between 2020 and 2025 for modeling and correcting brain deformation, with a particular focus on learning-based approaches. A comprehensive literature search was conducted in PubMed, IEEE Xplore, Scopus, and Web of Science, with predefined inclusion and exclusion criteria focused on computational methods applied to brain deformation compensation for neurosurgical imaging, resulting in $46$ studies meeting these criteria. We provide a unified analysis of methodological strategies, including deep learning-based image registration, direct deformation field regression, synthesis-driven multimodal alignment, resection-aware architectures addressing missing correspondences, and hybrid models that integrate biomechanical priors. We also examine dataset utilization, reported evaluation metrics, validation protocols, and how uncertainty and generalization have been assessed across studies. While learning-based deformation models demonstrate promising performance and computational efficiency, current approaches exhibit limitations in out-of-distribution robustness, standardized benchmarking, interpretability, and readiness for clinical deployment. Our review highlights these gaps and outlines opportunities for future research aimed at achieving more robust, generalizable, and clinically translatable deformation compensation solutions for neurosurgical guidance. By organizing recent advances and critically assessing evaluation practices, this work offers a comprehensive reference for researchers and clinicians working on data-driven brain deformation modeling and correction.

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