i will discuss joint work with gabriele di cerbo 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, if the dimension is less than 4. in higher dimensions, the same statement can be deduced assuming the bab conjecture. if time permits, i will discuss applications of this result to elliptically fibered calabi-yau manifolds.