Using V-filtrations, Kashiwara and Malgrange constructed Riemann-Hilbert correspondence for nearby and vanishing cycles along a single holomorphic functions. Sabbah then constructed multi V-filtrations along a finite set of holomorphic functions and thus obtained the multivariate Bernstein-Sato polynomials. However, Sabbah's method also indicates that the method of Kashiwara and Malgrange can not be generalized to the multivariate case in general. In this talk, first I will explain the construction of Bernstein-Sato ideals and Alexander complexes by using Mellin transformations. Then, I will focus on the construction of Riemann-Hilbert correspondence for Alexander complexes (the multivariate generalization of nearby cycles) by using Bernstein-Sato ideals and relative holonomic D-modules.