Elucidating quantum systems theory in terms of symmetry principles has triggered us in a number of recent advances: (1) it leads to a new handy controllability criterion, (2) it guides the design of quantum hardware, (3) it governs which quantum system can simulate another one given, and (4) it specifies the limit between time-optimal control and relaxation-optimised control of open systems. How principles turn into practice has been illustrated in the talk by a plethora of examples showing practical applications in solid-state devices, circuit-QED, and in spin systems. The algorithmic tools have been presented in a unified programming framework.