If the universe is a quantum mechanical system it has a quantum state. This state supplies a probabilistic measure for alternative histories of the universe. During eternal inflation these histories typically develop large inhomogeneities that lead to a mosaic structure on superhorizon scales consisting of homogeneous patches separated by inflating regions. As observers we do not see this structure directly. Rather our observations are confined to a small, nearly homogeneous region within our past light cone. This talk will describe how the probabilities for these observations can be calculated from the probabilities supplied by the quantum state without introducing a further ad hoc measure. The talk will emphasize the principles behind this result --- a quantum state, quantum spacetime leading to an ensemble of classical histories, quantum observers, a focus in local observations, and the use of coarse-grainings adapted to these observations. The principles will be illustrated in simple models in particular using the no-boundary wave function as a model of the quantum state. Applied to a model landscape we obtain specific predictions for features of the CMB spectrum and improvements in the `anthropic' bounds on the cosmological constant.