Mucopolysaccharidosis type I (MPS I) is a lysosomal storage disorder characterized by α‐L‐iduronidase deficiency. Patients present with a broad spectrum of disease severity ranging from the most severe phenotype (Hurler) with devastating neurocognitive decline, bone disease and early death to intermediate (Hurler‐Scheie) and more attenuated (Scheie) phenotypes, with a normal life expectancy. The most severely affected patients are preferably treated with hematopoietic stem cell transplantation, which halts the neurocognitive decline. Patients with more attenuated phenotypes are treated with enzyme replacement therapy. There are several challenges to be met in the treatment of MPS I patients. First, to optimize outcome, early recognition of the disease and clinical phenotype is needed to guide decisions on therapeutic strategies. Second, there is thus far no effective treatment available for MPS I bone disease. The pathophysiological mechanisms behind bone disease are largely unknown, limiting the development of effective therapeutic strategies. This article is a state of the art that comprehensively discusses three of the most urgent open issues in MPS I: early diagnosis of MPS I patients, pathophysiology of MPS I bone disease, and emerging therapeutic strategies for MPS I bone disease.