The Advanced Technology Large Aperture Space Telescope (ATLAST) team has identified five key technologies to enable candidate architectures for the future large-aperture ultraviolet/optical/infrared (LUVOIR) space observatory envisioned by the NASA Astrophysics 30-year roadmap, Enduring Quests, Daring Visions. The science goals of ATLAST address a broad range of astrophysical questions from early galaxy and star formation to the processes that contributed to the formation of life on Earth, combining general astrophysics with direct-imaging and spectroscopy of habitable exoplanets. The key technologies are: internal coronagraphs, starshades (or external occulters), ultra-stable large-aperture telescopes, detectors, and mirror coatings. Selected technology performance goals include: 1x10-10 raw contrast at an inner working angle of 35 milli-arcseconds, wavefront error stability on the order of 10 pm RMS per wavefront control step, autonomous on-board sensing and control, and zero-read-noise single-photon detectors spanning the exoplanet science bandpass between 400 nm and 1.8 μm. Development of these technologies will provide significant advances over current and planned observatories in terms of sensitivity, angular resolution, stability, and high-contrast imaging. The science goals of ATLAST are presented and flowed down to top-level telescope and instrument performance requirements in the context of a reference architecture: a 10-meter-class, segmented aperture telescope operating at room temperature (~290 K) at the sun-Earth Lagrange-2 point. For each technology area, we define best estimates of required capabilities, current state-of-the-art performance, and current Technology Readiness Level (TRL) – thus identifying the current technology gap. We report on current, planned, or recommended efforts to develop each technology to TRL 5.