In this talk I will discuss the question of how to characterize, in an operationally meaningful way, the inevitable disturbance of a quantum system in a measurement. I will review some well-known limitations of quantum measurements (facts), and give precise formulations of trade-off relations between information gain and disturbance. Famous examples among these limitations are the uncertainty principle, the complementarity principle, and Wigners theorem on limitations on measurements imposed by conservation laws. The universal validity of each of these has been challenged repeatedly, and no conclusive resolution seems to have been reached.
I will analyze some long-standing conflations and misconceptions (myths) concerning these quantum limitations, such as the reduction of the uncertainty principle to the idea of mechanical disturbance (momentum kicks), the claim that the uncertainty principle has nothing to do with (the impossibility of) simultaneous measurements of noncommuting quantities, and some alleged violations of the uncertainty and complementarity principles. Recent rigorous work has led to apparently contradictory conclusions on these issues. I will show that the contradictions dissolve if due attention is paid to the choice of operationally meaningful notions of measurement accuracy and disturbance.