Experimental methods to deposit layers just one atom or one unit cell thick include physical methods, such as molecular beam epitaxy, pulsed laser deposition and magnetron and ion beam sputtering, as well as chemical methods such as atomic layer deposition and chemical vapor deposition. Theoretical methods to simulate the growth of such materials and to calculate their properties are powerful and accurate enough that, by using these methods in tandem with experiment, rapid advances in atomically engineered materials with novel and technologically relevant properties is currently possible. Atomically engineered materials underpin the fields of spintronics, oxide electronics, cognitive devices and routes to room temperature superconductors.