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Breast cancer remains a leading cause of cancer-related mortality among women worldwide, underscoring the importance of effective screening strategies for early detection and improved survival. Although conventional modalities such as mammography reduce mortality, they are limited by false positives, false negatives, and overdiagnosis, particularly in dense breast tissue and diverse populations. Deep learning, especially convolutional neural networks (CNNs), has shown promise in improving diagnostic accuracy and reducing inter-reader variability; however, its translation into routine clinical practice requires critical evaluation beyond reported performance metrics. This critical review evaluates CNN-based deep learning applications for breast cancer detection across mammography, ultrasound, and MRI, with emphasis on training strategies and barriers to clinical deployment. A targeted literature search identified peer-reviewed studies focusing on CNN architectures, transfer learning, and implementation challenges. Findings indicate that models such as ResNet, DenseNet, and EfficientNet perform well in controlled settings, supported by transfer learning and data augmentation approaches. However, these results often fail to translate into consistent clinical performance, particularly across imaging modalities and real-world workflows. Limitations including demographic bias, insufficient external validation, and weak evidence of outcome or cost-effectiveness highlight a substantial gap between experimental success and clinical readiness. The review concludes that while deep learning in breast imaging is promising, its adoption should remain cautious and evidence-driven until robust clinical benefit is clearly demonstrated.