The aim of this work is to survey recent results on injective Banach lattices, outline a Boolean-valued approach, and pose some open problems. The central idea to the investigation is a Boolean-valued transfer principle from AL-spaces to injective Banach lattices: Every injective Banach lattice embeds into an appropriate Boolean-valued model, becoming an AL-space. To illustrate the method, a concrete description of injective Banach lattices similar to that of AL-spaces is presented.