Foundation models (FMs) are rapidly reshaping medical imaging, shifting the field from narrowly trained, task-specific networks toward large, general-purpose models that can be adapted across modalities, anatomies, and clinical tasks. In this review, we synthesize the emerging landscape of medical imaging FMs along three major axes: principles of FM design, applications of FMs, and forward-looking challenges and opportunities. Taken together, this review provides a technically grounded, clinically aware, and future-facing roadmap for developing FMs that are not only powerful and versatile but also trustworthy and ready for responsible translation into clinical practice.