Atomtronics is an emerging field that aims to manipulate ultracold atom moving in matter-wave circuits for fundamental studies in both quantum science and technological applications. In this Colloquium, recent progress in matter-wave circuitry and atomtronics-based quantum technology is reviewed. After an introduction to the basic physical principles and the key experimental techniques needed to realize atomtronic systems, the physics of matter waves in simple circuits such as ring traps and two-terminal systems is described. The main experimental observations and outstanding questions are discussed. Also presented are possible applications to a broad range of quantum technologies, from quantum sensing with atom interferometry to future quantum simulation and quantum computation architectures.