  A \emph{gerechte framework} is a partition of an $n \times n$ array into $n$
regions of $n$ cells each. A \emph{realization} of a gerechte framework is a
latin square of order $n$ with the property that when its cells are partitioned
by the framework, each region contains exactly one copy of each symbol. A
\emph{gerechte design} is a gerechte framework together with a realization.
  We investigate gerechte frameworks where each region is a rectangle. It seems
plausible that all such frameworks have realizations, and we present some
progress towards answering this question. In particular, we show that for all
positive integers $s$ and $t$, any gerechte framework where each region is
either an $s \times t$ rectangle or a $t\times s$ rectangle is realizable.
