For two infinite sequences $A$ and $B$ of non-negative integers, if every sufficiently large integer can be expressed as the sum of two elements taken from $A$ and $B$, then we call such $A$, $B$ additive complements. In this talk, we will present a review of our results (joint with Prof. Yong-Gao Chen) on additive complements. Furthermore, some open conjectures are also posed.