  We study the phase retrieval problem for the short-time Fourier transform on
the groups $\mathbb{Z}$, $\mathbb{Z}_d$ and $\mathbb{R}^d$. As is well-known,
phase retrieval is possible, once the window's ambiguity function vanishes
nowhere. However, there are only few results for windows which don't meet this
condition. The goal of this paper is to establish new and complete
characterizations for phase retrieval with more general windows and compare
them to existing results. For a fixed window, our uniqueness conditions usually
only depend on the signal's support and are therefore easily comprehensible.
Additionally, we discuss sharpness of both new and existing results by looking
at various examples along the way.
