  Quantum computation offers a promising new kind of information processing,
where the non-classical features of quantum mechanics can be harnessed and
exploited. A number of models of quantum computation exist, including the now
well-studied quantum circuit model. Although these models have been shown to be
formally equivalent, their underlying elementary concepts and the requirements
for their practical realization can differ significantly. The new paradigm of
measurement-based quantum computation, where the processing of quantum
information takes place by rounds of simple measurements on qubits prepared in
a highly entangled state, is particularly exciting in this regard. In this
article we discuss a number of recent developments in measurement-based quantum
computation in both fundamental and practical issues, in particular regarding
the power of quantum computation, the protection against noise (fault
tolerance) and steps toward experimental realization. Moreover, we highlight a
number of surprising connections between this field and other branches of
physics and mathematics.
