Two large prospective trials—MASAI (n=105,934, Sweden) and PRAIM (n=461,818, Germany)—have demonstrated that AI-assisted screening significantly improves cancer detection, reporting increases of 29% and 17.6% respectively. Despite these gains, the reduction in interval cancers remains modest (1.55 vs. 1.76 per 1,000 screens in MASAI), and aggressive subtypes such as triple-negative breast cancer remain largely undetected. While factors such as cancer growth kinetics, imaging physics, and screening intervals contribute to this residual burden, this survey argues that one plausible limiting factor is architectural: supervised convolutional systems are trained on discrete radiological labels that exclude the pre-malignant tissue signals responsible for interval cancers. Self-supervised learning (SSL) avoids this by deriving training signal from unlabelled image structure. Four classes of self-supervised learning techniques applicable to mammography are compared—contrastive learning (SimCLR/MoCo), masked autoencoders (MAE), self-distillation (DINO), and vision-language pre-training (CLIP)—along three axes: training mechanism, data requirements, and resistance to scanner-induced domain shift. We review domain-specific foundation models including MammoDINO, Mammo-CLIP, MAMA, Mammo-FM, and VersaMammo, analyse how each addresses the generalisation gap, discuss interpretability requirements for clinical deployment, and outline the research directions most likely to reduce the residual interval cancer burden.