In this talk, we shall introduce our series of work concerning cancellation in additively twisted sums on GL(m). We prove cancellation in these twisted sums for all automorphic L-function on GL(m), uniformly in the twisted parameter. The proof of this series of work relies on the generalized Bourgain-Sarnak-Ziegler criterion, the method of Montgomery and Vaughan, the sieve method, and the theory of automorphic L-functions. This talk is based on joint work with Yujiao Jiang and Zhiwei Wang.