The Space and Terrestrial Robotic Exploration (SpaceTREx) Laboratory at University of Arizona's Aerospace and Mechanical Engineering Department develop systems engineering design and control solutions for space, planetary and asteroid exploration, using small spacecraft, robots and sensor network devices. Research is focused on developing enabling technologies for extreme environment exploration, interplanetary CubeSat explorers and on-orbit servicing spanning spacecraft constellations, propulsion, power and communications. The laboratory and key personnel have a diverse range of expertise including CubeSat design, development, launch expertise, smart system design and control using bio-inspired and neural network control paradigms, space weather and extreme-environment robotics. The laboratory is rapidly expanding and diversifying its research portfolio by exploiting new developments in terrestrial technology, particularly nanotechnology and applying it to space exploration, while taking technology developed for space and applying it towards important challenges facing humanity in the fields of climate change, security, water and energy.