The “science of consciousness” and quantum physics share many similarities, in particular when “measurements” or “observations” are concerned. In quantum theory, a measurement or observation is an intervention which not only produces a recorded value but also changes the state of the measured system. As a consequence, observations do not “commute”, i.e. the results of successive observations typically depend on their sequence. An additional consequence is “contextuality”: The result of an observation depends on which other observations are (or could be) performed. The mathematical formalism of quantum theory takes this into account. For about twenty years the same formal framework has been applied to areas such as psychology, cognitive sciences, economics etc. In numerous situations the obtained theoretical models match empirical results with astonishing accuracy. In my talk I will sketch the key features of this formalism and point out some similarities and differences between consciousness and quantum physics.