Unsupervised anomaly detection (UAD) based on deep generative modelling has been increasingly explored for identifying pathological brain abnormalities without requiring voxel-level annotations. By learning the distribution of healthy anatomy and generating pseudo-healthy reconstructions, these methods aim to localise deviations in a pathology-agnostic manner. Despite rapid methodological development - from autoencoders and variational autoencoders to generative adversarial networks and diffusion-based models - a structured synthesis of their application in structural neuroimaging is lacking. We conducted a PRISMA-ScR-guided scoping review of studies published between January 2018-December 2025 that applied unsupervised deep generative models to anomaly detection in brain MRI (and, less frequently, CT). Thirty-three studies met inclusion criteria. Methods were categorised by architectural family, and reported performance was synthesised across major pathology groups, with segmentation (Dice) and detection metrics (AUROC, AUPRC) disaggregated by evaluation level (voxel, slice, subject). For transparency, we also summarised dataset characteristics, dimensionality (2D vs. 3D), and thresholding strategies. Overall, unsupervised generative approaches demonstrate potential for pathology-agnostic anomaly localisation, particularly in settings where annotated data are scarce. However, methodological heterogeneity, limited external validation, and sensitivity to dataset characteristics remain important challenges. Emerging paradigms - including anatomy-aware modelling, diffusion-based frameworks, and alternative normative evaluation metrics - seek to address these limitations and improve robustness and clinical relevance.