Significant optical engineering advances at the University of Arizona are being made for design, fabrication, and construction of next generation astronomical telescopes. This summary review paper focuses on the technological advances in three key areas. First is the optical fabrication technique used for constructing next-generation telescope mirrors. Advances in ground-based telescope control and instrumentation comprise the second area of development. This includes active alignment of the laser truss-based Large Binocular Telescope (LBT) prime focus camera, the new MOBIUS modular cross-dispersion spectroscopy unit used at the prime focal plane of the LBT, and topological pupil segment optimization. Lastly, future space telescope concepts and enabling technologies are discussed. Among these, the Nautilus space observatory requires challenging alignment of segmented multi-order diffractive elements. The OASIS terahertz space telescope presents unique challenges for characterizing the inflatable primary mirror, and the Hyperion space telescope pushes the limits of high spectral resolution, far-UV spectroscopy. The Coronagraphic Debris and Exoplanet Exploring Pioneer (CDEEP) is a Small Satellite (SmallSat) mission concept for high-contrast imaging of circumstellar disks and exoplanets using vector vortex coronagraph. These advances in optical engineering technologies will help mankind to probe, explore, and understand the scientific beauty of our universe.