Automorphic L-functions are fundamental invariants attached to a given cuspidal automorphic representation of a reductive group G. In addition to arithmetic applications, automorphic L-functions are used to characterize various types of Langlands functorial transfers. In this lecture, I will discuss some basic cases of the theory, including the automorphic descent endoscopy correspondence via automorphic integral transforms, and report my recent work on the twisted version of automorphic descent.