  We introduce quantum history states and their mathematical framework, thereby
reinterpreting and extending the consistent histories approach to quantum
theory. Through thought experiments, we demonstrate that our formalism allows
us to analyze a quantum version of history in which we reconstruct the past by
observations. In particular, we can pass from measurements to inferences about
"what happened" in a way that is sensible and free of paradox. Our framework
allows for a richer understanding of the temporal structure of quantum theory,
and we construct history states that embody peculiar, non-classical
correlations in time.
