Phase retrieval is widely used in optics, X-ray crystallography, holographic imaging and other applications, it is one of the new research topic in applied and computational harmonic analysis. In this talk, I will introduce some results on phase retrieval in shift-invariant spaces, and the stable phase retrieval in infinite-dimensional spaces. I will also introduce a new phase retrieval paradigm in the vector-valued setting, which is motivated by complex conjugate phase retrieval of vectors in the complex range space of a real matrix and functions in the complex Paley-Wiener space, and also by determination of a vector field defined on a graph from their relative magnitudes between neighboring vertices.