  Magnonics and magnon spintronics aim at the utilization of spin waves and
magnons, their quanta, for the construction of wave-based logic networks via
the generation of pure all-magnon spin currents and their interfacing with
electrical charge transport. The promise of efficient parallel data processing
and low power consumption renders this field one of the most promising research
areas in spintronics. In this context, the process of parallel parametric
amplification, i.e., the conversion of microwave photons into magnons at one
half of the microwave frequency, has proven to be a versatile tool. Its
beneficial and unique properties, such as frequency and mode-selectivity, the
possibility to excite spin waves in a wide wavevector range and the creation of
phase-correlated wave pairs, render it one of the key methods of spin-wave
generation and amplification.
  The application of parallel parametric amplification to micro- and
nanostructures is an important step towards the realization of magnonic
networks. This is motivated not only by the fact that amplifiers are an
important tool for the construction of any extended logic network but also by
the unique properties of parallel parametric amplification, such as a
phase-dependent amplification. Recently, the successful application of parallel
parametric amplification to metallic microstructures has been reported. It has
been demonstrated that parametric amplification provides an excellent tool to
generate and to amplify spin waves in these systems. In particular, the
amplification greatly benefits from the discreteness of the spin-wave spectra.
This opens up new, interesting routes of spin-wave amplification and
manipulation. In this Review, we give an overview over the recent developments
and achievements in this field.
