Fabry disease is an X-linked inherited lysosomal disorder that causes accumulation of glycosphingolipids in body fluids and tissues, leading to progressive organ damage and reduced life expectancy. It can affect both males and females and can be classified into classic or later-onset phenotypes. In classic Fabry disease, α-galactosidase A (α-Gal A) activity is absent or severely reduced and disease manifestations have an early onset that can affect multiple organs. In contrast, in later-onset Fabry disease, patients have residual α-Gal A activity and clinical features are primarily confined to the heart. Individualized therapeutic goals in Fabry disease are required due to varying phenotypes and patient characteristics, and the wide spectrum of disease severity. An international group of expert physicians convened to discuss and develop practical clinical recommendations for disease- and organ-specific therapeutic goals in Fabry disease, based on expert consensus and evidence identified through a structured literature review. Biomarkers reflecting involvement of various organs in adult patients with classic Fabry disease are discussed and consensus recommendations for disease- and organ-specific therapeutic goals are provided. These consensus recommendations should support the establishment of individualized approaches to the management of patients with classic Fabry disease by considering identification, diagnosis, and initiation of disease-specific therapies before significant organ involvement, as well as routine monitoring, to reduce morbidity, optimize patient care, and improve patient health-related quality of life.