Substitution of diseased organ/tissues with totally artificial machines or transplantable biohybrid devices where functionally competent cells are enveloped within immunoprotective artificial membranes could represent one of the future goals in medicine. In particular, artificial or, closer to feasibility, biohybrid artificial pancreas (BHAP) could replace the function of pancreatic islet β-cells that have been destroyed by autoimmunity, thereby obviating the need to treat patients with type 1 diabetes mellitus (T1DM) with multiple daily insulin injections. State-of-the-art diabetes therapy and perspectives in the use of BHAP, with special regard to islet-cell-containing microcapsules fabricated with alginate-based polymers, including applications to experimental animal models according to different chemical procedures, are reviewed. Special emphasis has been given to preparation methods, immunoprotection strategies, and biocompatibility of the islet-cell-containing microbarriers, as well as to approaches to ameliorate these features. Currently available BHAP prototypes have been critically reviewed to define expectations about the next generation devices targeting the final cure of T1DM.