A Calabi-Yau variety is a normal projective variety with numerically trivial canonical divisor K_X. The index of a Calabi-Yau variety X is defined as the smallest positive integer m such that mK_X is trivial. A fundamental open problem in this area, known as the index conjecture, suggests that for Calabi-Yau varieties of fixed dimension and with appropriate assumptions on singularities (such as log canonical), their indices are bounded. In this talk, I will discuss recent developments in understanding the relationship between the indices of smooth Calabi-Yau varieties and the indices of lower-dimensional log Calabi-Yau pairs. This approach gives an inductive framework that may lead to a proof of the index conjecture.