In this talk we will discuss our recent results, obtained in joint work with Harris, Lin and also with Raghuram, on Deligne's Conjecture for motivic L-functions over CM-fields. While our original result has been dependent on a difficult non-vanishing conjecture for twisted automorphic standard L-functions, we will report in this talk on how to remove this conjecture from our hypotheses by a strategy inspired by the recent work of Chen.