The twisted K-theory of compact simple Lie groups has been a subject of much study because of its connection with the WZW (Wess-Zumino-Witten) model in quantum field theory. It it is known that for non-zero twists, the twisted K-theory is always a finite cyclic group tensored with an exterior algebra over Z, but that the order of the torsion is given by a very complicated formula which is very difficult to prove. We go back to this problem yet again and make a number of new observations. First, if one compact simple Lie group covers another, then the map on H^3 induced by the covering is always multiplication by either 1 or 2 (from one infinite cyclic group to another), but which it is depends in a complicated way on the groups involved. From this we can make some work of Daenzer-Van Erp and Bunke-Nikolaus more explicit. We also give an elementary proof away from finitely many primes of the formula for the order of the torsion of the twisted K-groups. This is all joint work with Varghese Mathai.