The strategic astrophysics missions of the coming decades will help answer the questions "How did our universe begin and evolve?" "How did galaxies, stars, and planets come to be?" and "Are we alone?" Enabling these missions requires advances in key technologies far beyond the current state of the art. NASA’s Physics of the Cosmos2 (PCOS), Cosmic Origins3 (COR), and Exoplanet Exploration Program4 (ExEP) Program Offices manage technology maturation projects funded through the Strategic Astrophysics Technology (SAT) program to accomplish such advances. The PCOS and COR Program Offices, residing at the NASA Goddard Space Flight Center (GSFC), were established in 2011, and serve as the implementation arm for the Astrophysics Division at NASA Headquarters. We present an overview of the Programs' technology development activities and the current technology investment portfolio of 23 technology advancements. We discuss the process for addressing community-provided technology gaps and Technology Management Board (TMB)-vetted prioritization and investment recommendations that inform the SAT program. The process improves the transparency and relevance of our technology investments, provides the community a voice in the process, and promotes targeted external technology investments by defining needs and identifying customers. The Programs’ priorities are driven by strategic direction from the Astrophysics Division, which is informed by the National Research Council’s (NRC) "New Worlds, New Horizons in Astronomy and Astrophysics" (NWNH) 2010 Decadal Survey report , the Astrophysics Implementation Plan (AIP)  as updated, and the Astrophysics Roadmap “Enduring Quests, Daring Visions” . These priorities include technology development for missions to study dark energy, gravitational waves, X-ray and inflation probe science, and large far-infrared (IR) and ultraviolet (UV)/optical/IR telescopes to conduct imaging and spectroscopy studies. The SAT program is the Astrophysics Division’s main investment method to mature technologies that will be identified by study teams set up to inform the 2020 Decadal Survey process on several large astrophysics mission concepts.