Foundation models, pretrained on diverse data, objectives, or modalities for reuse across downstream tasks, are increasingly applied to medical image analysis. Their performance depends not only on pretraining but also on how they are adapted to specific tasks, data regimes, and deployment settings. Whereas previous reviews have considered adaptation within broader syntheses, this review focuses specifically on post-pretraining interventions applied to existing FMs. Using a structured narrative review with a systematic, auditable workflow, we identified 719 eligible reports representing 705 independent studies. Of these, 473 provided controlled comparative evidence: 322 formally published studies formed the primary synthesis and 151 preprint-only studies a sensitivity layer. Adaptation was organized into five non-mutually exclusive families: parameter-level, representation-level, objective-level, data-centric, and architectural/sequence-level adaptation, with model use and update regime analyzed separately. Controlled comparisons showed no consistent ranking among frozen, parameter-efficient, partial, or full updating, or across broader adaptation families; outcomes varied by task, data regime, comparator, and evaluation setting. Clinical-readiness evidence remained limited: 173/705 studies (24.5\%) had confirmed independent external validation, 10 (1.4\%) reported calibration or uncertainty evidence, and 97/322 formally published comparative studies (30.1\%) included a qualifying externally validated arm. Overall, FM adaptation is a context-dependent design space rather than a hierarchy of preferred strategies.

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