  Some measurements in quantum mechanics disturb each other. This has puzzled
physicists since the formulation of the theory, but only in recent decades has
the incompatibility of measurements been analyzed in depth and detail, using
the notion of joint measurability of generalized measurements. In this
Colloquium joint measurability and incompatibility are reviewed from the
perspective of quantum information science. The Colloquium starts by discussing
the basic definitions and concepts. An overview on applications of
incompatibility, such as in measurement uncertainty relations, the
characterization of quantum correlations, or information processing tasks like
quantum state discrimination, is then presented. Finally, emerging directions
of research, such as a resource theory of incompatibility as well as other
concepts to grasp the nature of measurements in quantum mechanics, are
discussed.
