  The large electric dipole moments associated with highly excited Rydberg
states of atoms and molecules make gas-phase samples in these states very well
suited to deceleration and trapping using inhomogeneous electric fields. The
methods of Rydberg-Stark deceleration with which this can be achieved are
reviewed here. Using these techniques, the longitudinal motion of beams of
atoms and molecules moving at speeds as high as 2500~m/s have been manipulated,
with changes in kinetic energy of up to $|\Delta
E_{\mathrm{kin}}|=1.3\times10^{-20}$~J ($|\Delta E_{\mathrm{kin}}|/e=80$~meV or
$|\Delta E_{\mathrm{kin}}|/hc=650$~cm$^{-1}$) achieved, while decelerated and
trapped samples with number densities of $10^6$--$10^7$~cm$^{-3}$ and
translational temperatures of $\sim150$~mK have been prepared. Applications of
these samples in areas of research at the interface between physics and
physical chemistry are discussed.
