Biological aging is increasingly understood as a heterogeneous, multi-system process marked by organ-level vulnerability, cross-organ coordination, and variation in resilience. Advances in plasma proteomics, metabolomics, imaging, DNA methylation, digital biomarkers, and genetic epidemiology have enabled organ-level, system-level, and cross-organ age models, but these measures are often interpreted more strongly than the evidence permits. In this Review, we synthesize evidence on biological age models derived from molecular, imaging, digital, clinical, and multi-omic data and introduce ORGAN-AGE as an interpretive framework for judging what these signals can and cannot establish. We distinguish organ-derived, organ-enriched, organ-informative, system-informative, and systemic biomarkers, because circulating molecular signals rarely prove tissue origin. We critically evaluate how age gaps are constructed, bias-corrected, validated, interpreted, and linked to mortality, frailty, dementia, cardiovascular disease, diabetes complications, multimorbidity, and functional decline. A central argument is that organ age gaps can localize apparent aging burden, whereas cross-organ coupling should be treated as a graded inference rather than evidence of direct biological propagation unless longitudinal, molecular, genetic, functional, or experimental support is available. Resilience should likewise be operationalized through recovery, adaptation, and trajectory change rather than inferred from static biomarkers alone. Finally, we outline a staged translational roadmap in which organ aging models may support risk interpretation, trial enrichment, target prioritization, and future digital-twin research only after calibration, transportability, incremental utility, and clinical end-use have been demonstrated.