  Phase retrieval has become a very active area of research. We will classify
when phase retrieval by Parseval frames passes to the Naimark complement and
when phase retrieval by projections passes to the orthogonal complements. We
introduce a new concept we call norm retrieval and show that this is what is
necessary for passing phase retrieval to complements. This leads to a detailed
study of norm retrieval and its relationship to phase retrieval. One
fundamental result: a frame $\{\varphi_i\}_{i=1}^M$ yields phase retrieval if
and only if $\{T\varphi_i\}_{i=1}^M$ yields norm retrieval for every invertible
operator $T$.
