In many systems for which there are several atoms in the unit cell, the displacements of the atoms may be locally correlated even though there is no long range coherence. Such displacements can play an important role in determining various macroscopic properties. We consider several examples to demonstrate this phenomena - the local distortions in the colossal magneto-resistive (CMR) and charge-ordered manganites, magnetic field induced distortions in CMR materials that are connected to macroscopic magnetostriction, and correlated displacements of tetrahedral units within the negative thermal expansion material ZrW2O8. The distortions in the CMR materials observed using XAFS change rapidly just below Tc and are attributed to the formation of polarons as the temperature is increased through Tc. In the ferromagnetic state, the lattice is more ordered for CMR systems; consequently applying a magnetic field for T ∼ Tc should decrease the local distortions. Such an effect has been observed and is a much larger effect than the measured macroscopic magnetostriction. Finally, in ZrW2O8 the tetrahedral and octahedral units are found to be very rigid as expected. More surprising is that the width of the pair-distance distribution for the W-Zr atom-pair is also quite small, indicating that the W-Zr linkage is stiff. In contrast, for the W-W pair, the distribution width grows rapidly with T, indicating correlated displacements of two WO4 tetrahedral units.