Background: Family-centered care is a core principle of contemporary pediatric rehabilitation, particularly for children with neurodevelopmental disorders. Conceptual frameworks emphasizing functioning, participation, and contextual factors are essential to operationalize this approach in clinical practice. The International Classification of Functioning, Disability and Health (ICF) and the F-words framework are widely used models aligned with these principles; however, their practical integration remains challenging. Methods: A narrative literature review was conducted using PubMed, Scopus, and Web of Science databases to identify English-language publications (2005–2025) addressing the ICF, the F-words framework, and pediatric neurodevelopmental disability. Results: Thirty-one publications were included. The findings indicate increasing international adoption of both frameworks in pediatric rehabilitation. However, persistent challenges were identified, including conceptual ambiguity between activity and participation domains, limited operationalization of personal factors, overlap between the ICF and F-words constructs, limited standardization, difficulties in outcome measurement, and inconsistent involvement of families in clinical decision-making. Conclusions: The ICF and the F-words framework offer complementary strengths for advancing family-centered pediatric care. A structured dual-layer integration approach may enhance shared decision-making, clarify goal-setting, and improve communication with families. Further methodological refinement and practice-oriented guidance are needed to support consistent clinical implementation.