We review some of the theoretical techniques developed in the past decade to study Rydberg spectroscopy and dynamics. These techniques can be used to calculate not only the transition energies and the spectral intensities but also the dynamical quantities, such as radiative lifetimes and collision cross sections, of high Rydberg states. Both aspects of spectroscopy and dynamics are discussed and are mainly based on our previous research results. Using the inverse Born-Oppenheimer approximation (IBOA) to establish a basis set, we have calculated the absorption rates for the resonance two-photon (R2P) and non-resonance two-photon (NR2P) zero kinetic energy (ZEKE) or mass analyzed threshold ionization (MATI) spectroscopy. The resonance VUV-IR and IR-VUV two-photon spectra are discussed separately to emphasize their respective utilities. For comparison, the formulas to analyze the recently proposed one-photon (1P) ZEKE spectroscopy are also presented using the IBOA. To study the Rydberg dynamics, we have calculated the spontaneous emission rates and the blackbody radiation induced transition rates to establish a reference time scale for high Rydberg states. Due to the large size of a Rydberg atom, the inelastic collision cross sections are significant. We have thus calculated the cross sections for a Rydberg atom in collision with an ion using the Born approximation. We also show how to calculate the transition probabilities of autoionization due to the breakdown of the IBOA. To analyze both the vibronic spectra and dynamical quantities for Rydberg molecules, we employ quantum chemistry calculation to obtain the potential surfaces of molecules and their ions. These potential surfaces can then be used to calculate the Franck-Condon factors involved in the vibronic transitions. Several experimental spectra are analyzed with this theory. Buy this Article