In this talk I will overview a new gauge-theoretical approach to the Hull-Strominger system using holomorphic string algebroids. In the smooth setup, a string algebroid provides an infinitesimal version of a principal bundle for the string group. The main focus will be on the consequences of this approach for the existence and uniqueness problem, as well as for the moduli space metric. The discussion will be illustrated by a key example. Joint work with Rubio, Tipler, and Shahbazi.