ABSTRACT: I will introduce the concept of monoidal gerbes and show how to use them to twist suitable monoidal tensor categories. We will see interesting examples of this construction related to moduli stacks of objects in Calabi-Yau categories. For 3-Calabi-Yau categories we can go even further by constructing interesting monoidal functors. This allows us to define the Cohomological Hall (co)Algebra.