Genetic disease can lead to myocardial infiltration which results in a cardiomyopathy characterized by the deposition of storage products within ventricular walls. The storage is inducing diastolic filling abnormalities which are finally responsible for the symptoms such as dyspnoea. During follow-up most patients die because of heart failure. Transthyretin-related amyloidosis is the most common infiltrative cardiomyopathy. Rarer diseases are storage disorders such as Fabry disease and Pompe disease. The primary neurological disease Friedreich’s ataxia can in addition induce an infiltrative cardiomyopathy. This chapter focuses on the pathophysiology, the symptoms, the typical image findings, and the potential treatment of these different rare genetic infiltrative diseases.