Positive operator valued measures (POVMs) have an important physical significance, as they represent the generalized observables in the quantum theory of measurement and in its applications, such as quantum optics or theory of measurement in phase-space, which are called generalized measurements in quantum mechanics. So POVMs provide some basic mathematical tools in quantum information theory. A special class of POVMs, namely frame POVMs, is induced by Hilbert space frames. Such a POVM, due to its simplicity, plays special roles in applications including the quantum detection problem in quantum information theory and the phase retrieval problem in engineering. In this chapter, we review some basics and present some of our recent work related to quantum detection and phase retrievable frames.