  \begin{abstract} In this manuscript, we answer a list of longstanding open
problems on weak phase retrieval including: (1) A complete classification of
the vectors $\{x_i\}_{i=1}^2$ in $\RR^3$ that do weak phase retrieval; (2) We
show that frames doing weak phase retrieval in $\RR^n$ must span $\RR^n$; (3)
We give an example of a set of vectors doing phase retrieval but their
orthogonal complement hyperplanes fail weak phase retrieval; (4) We give a
classification of weak phase retrievable frames - which makes clear the
difference between phase retrieval and weak phase retrieval; (5) We classify
when weak phase retrievable frames also do norm retrieval. We then introduce
the notion of weak phase retrieval by projections and develop their basic
properties. We then look at phase (norm) retrieval by projections. We end with
some open problems.
  We provide numerous examples to show that our results are best possible.
\end{abstract}
