  Using model theoretic techniques that proved that the class of $n$ neat
reducts of $m$ dimensional cylindric algebras, $\Nr_n\CA_m$, is not elementary,
we prove the same result for $\Ra\CA_k$, $k\geq 5$, and we show that
$\Ra\CA_k\subset S_c\Ra\CA_k$ for all $k\geq 5$. Conversely, using the rainbow
construction for cylindric algebra, we show that several classes of algebras,
related to the class $\Nr_n\CA_m$, $n$ finite and $m$ arbitrary, are not
elementary. Our results apply to many cylindric-like algebras, including
Pinter's substitution algebras and Halmos' polyadic algebras with and without
equality. The techniques used are essentially those used by Hirsch and
Hodkinson, and later by Hirsch in \cite{hh} and \cite{r}. In fact, the main
result in \cite{hh} follows from our more general construction. Finally we blow
up a little the {\it blow up and blur construction} of Andr\'eka nd N\'emeti,
showing that various constructions of weakly representable atom structures that
are not strongly representable, can be formalized in our blown up, blow up and
blur construction, both for relation and cylindric algebras. Two open problems
are discussed, in some detail, proposing ideas. One is whether class of subneat
reducts are closed under completions, the other is whether there exists a
weakly representable $\omega$ dimensional atom structure, that is not strongly
representable. For the latter we propose a lifting argument, due to Monk,
applied to what we call anti-Monk algebras (the algebras, constructed by Hirsch
and Hodkinson, are atomic, and their atom structure is stongly representable.)
