Foundation models (FMs) have emerged as a transformative paradigm in medical image analysis, offering the potential to provide generalizable, task-agnostic solutions across a wide range of clinical tasks and imaging modalities. Their capacity to learn transferable representations from large-scale data has the potential to address the limitations of conventional task-specific models. However, adaptation of FMs to real-world clinical practice remains constrained by key challenges, including domain shifts, limited availability of high-quality annotated data, substantial computational demands, and strict privacy requirements. This review presents a comprehensive assessment of strategies for adapting FMs to the specific demands of medical imaging. We examine approaches such as supervised fine-tuning, domain-specific pretraining, parameter-efficient fine-tuning, self-supervised learning, hybrid methods, and multimodal or cross-modal frameworks. For each, we evaluate reported performance gains, clinical applicability, and limitations, while identifying trade-offs and unresolved challenges that prior reviews have often overlooked. Beyond these established techniques, we also highlight emerging directions aimed at addressing current gaps. These include continual learning to enable dynamic deployment, federated and privacy-preserving approaches to safeguard sensitive data, hybrid self-supervised learning to enhance data efficiency, data-centric pipelines that combine synthetic generation with human-in-the-loop validation, and systematic benchmarking to assess robust generalization under real-world clinical variability. By outlining these strategies and associated research gaps, this review provides a roadmap for developing adaptive, trustworthy, and clinically integrated FMs capable of meeting the demands of real-world medical imaging.