  There are fundamental limits to the accuracy with which one can determine the
state of a quantum system. I give an overview of the main approaches to quantum
state discrimination. Several strategies exist. In quantum hypothesis testing,
a quantum system is prepared in a member of a known, finite set of states, and
the aim is to guess which one with the minimum probability of error. Error free
discrimination is also sometimes possible, if we allow for the possibility of
obtaining inconclusive results. If no prior information about the state is
provided, then it is impractical to try to determine it exactly, and it must be
estimated instead. In addition to reviewing these various strategies, I
describe connections between state discrimination, the manipulation of quantum
entanglement, and quantum cloning. Recent experimental work is also discussed.
