Abstract: Trapped, cold Rydberg atoms are important in future applications in high-precision measurement, field sensing and quantum information processing. The following topics will be discussed. (1) We use high-resolution atom imaging to measure the Rydberg-Rydberg correlation function in Rydberg-atom samples prepared within the spatially-varying light shifts of a laser trap. We study the pair-correlation behavior as well as direct two-photon excitation of correlated Rydberg-atom pairs in the trap. (2) We employ a standing-wave laser trap in combination with Rydberg-atom position control within the standing wave to show that optical photoionization of a Rydberg atom does not occur within the main lobes of the Rydberg electron’s wave-function, but only within a relatively small volume around the nucleus. This evidence is consistent with the (sometimes unexpected) validity of the electric-dipole approximation for optical Rydberg-atom photoionization. (3) Modulated, spatially inhomogeneous light fields, such as amplitude-modulated optical lattices, can be used to drive multipole microwave transitions between Rydberg levels in a minimally invasive manner. This enables high-precision measurements of atomic properties. I will show first results with this new type of spectroscopy. (4) High-precision spectroscopy will be most promising with circular, Bohr-like Rydberg states. These have long lifetimes and low electric polarizabilities, among other nice features. Towards this, we have recently produced and trapped such atoms with an adiabatic “crossed-fields” state-switching method. Looking ahead, I will briefly discuss how these methods could be combined to perform specific high-precision measurements.