I will discuss a joint work with Roberto Svaldi on boundedness of Calabi-Yau pairs. Recent works in the minimal model program suggest that pairs with trivial log canonical class should satisfy some boundedness properties. I will show that Calabi-Yau pairs which are not birational to a product are indeed log birationally bounded. This result can be thought as a first step towards boundedness to elliptically fibered Calabi-Yau manifolds.