Type 1 diabetes is commonly treated with the administration of insulin, either by multiple insulin injections or by a continuous supply of insulin through a wearable pump. Insulin therapy allows long-term survival in individuals with type 1 diabetes; however, it does not guarantee constant normal blood sugar control. Because of this, long-term type 1 diabetic survivors often develop vascular complications, such as diabetic retinopathy, an eye disease that can cause poor vision and blindness, and diabetic nephropathy, a kidney disease that can lead to kidney failure. Some individuals with type 1 diabetes develop hypoglycemia unawareness, a life-threatening condition that is not easily treatable with medication and is characterized by reduced or absent warning signals for hypoglycemia. For such individuals, transplantation of pancreatic islets is a possible treatment option. Unfortunately, insulin independence among islet transplant recipients tends to decline over time. New strategies aimed at promoting engraftment of transplanted islets are needed to improve the clinical outcomes associated with this procedure. The purpose of this study is determine the safety and efficacy of islet transplantation, when combined with an immunosuppressive medication regimen, for treating type 1 diabetes in individuals experiencing hypoglycemia unawareness and severe hypoglycemic episodes. This study will also seek to improve the understanding of determinants of success and failure of islet transplants for type 1 diabetes.