  In this book chapter, we provide a tutorial introduction to one-way quantum
computation and many of the techniques one can use to understand it. The
techniques which are described include the stabilizer formalism and the logical
Heisenberg picture. We highlight ways in which it is useful to understand
one-way computation beyond simple equivalence with the quantum circuit model.
We briefly review current proposals of implementations and experimental
progress and summarize some recent related theoretical developments.
  Although the chapter is primarily didactic in focus, we include a number of
new methods and observations. These include: a simpler and more compact
formulation of one-way quantum computation in the stabilizer formalism; A new
way of implementing unitaries diagonal in the computational basis; New results
on the family of operations which may be implemented in a single round of
measurements; A method for constructing compact one-way patterns by decomposing
unitaries in terms of diagonal unitaries and Clifford group transformations.
