  Octahedral tilting is key to the structure and functionality of perovskites.
Here we show how these distortions manifest in the related Prussian blue
analogues (PBAs): cyanide versions of double perovskites with formula
A$_x$M[M$^{\prime}$(CN)$_6$]$_{1-y}\Box _y\cdot n$H$_2$O (A = alkali metal, M
and M$^{\prime}$ = transition metals, $\Box$ = vacancy/defect). Tilts are
favoured by high values of $x$ if A = Na or K, whereas the transition metals
play a less important role. External hydrostatic pressure can induce tilt
transitions nearly irrespective of the stoichiometry, whereas thermal
transitions are only reported for $x>1$. Interstitial water can alter the
transitions induced by a different stimulus, but (de)hydration \textit{per se}
does not lead to tilts. Implications for rational design of critical
functionality -- including improper ferroelectricity and electrochemical
performance -- are discussed. The results are important for a fundamental
understanding of phase transitions as well as for the development of functional
materials based on PBAs.
