Advances in experimental technique allow application of pulsed unidirectional electric fields, termed half-cycle pulses (HCPs), to Rydberg atoms whose characteristic times are much less than the classical electron orbital period. In this limit each HCP simply delivers an impulsive momentum transfer, or "kick", to the excited electron. A number of protocols for controlling and manipulating Rydberg atom wavepackets using carefully-tailored sequences of HCPs will be described with emphasis on the production of quasi-one-dimensional and near circular Rydberg states, and on navigating electron wavepackets in phase space. A technique to probe reversible and irreversible dephasing based on electric dipole echoes will also be described. Insights provided by this work into atomic engineering, classical-quantum correspondence, the behavior of driven systems, and decoherence in mesoscopic quantum systems will be discussed.