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 |Δ E kin|=1.3×10-20 J (|Δ E kin|/e=80 meV or |Δ E kin|/h c=650 cm -1) achieved, while decelerated and trapped samples with number densities of 106- 107 cm -3 and translational temperatures of ∼150 mK have been prepared. Applications of these samples in areas of research at the interface between physics and physical chemistry are discussed.