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 to excite and to manipulate spin waves. 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, have enabled the achievement of important milestones like the magnon Bose Einstein condensation and the cloning and trapping of spinwave packets. Parallel parametric amplification, which allows for the selective amplification of magnons while conserving their phase is, thus, one of the key methods of spin-wave generation and amplification.The application of parallel parametric amplification to CMOS-compatible 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. In particular, the creation of phase-correlated wave pairs allows for rewarding alternative logic operations such as a phase-dependent amplification of the incident waves. Recently, the successful application of parallel parametric amplification to metallic microstructures has been reported which constitutes an important milestone for the application of magnonics in practical devices. It has been demonstrated that parametric amplification provides an excellent tool to generate and to amplify spin waves in these systems in a wide wavevector range. In particular, the amplification greatly benefits from the discreteness of the spin-wave spectra since the size of the microstructures is comparable to the spin-wave wavelength. This opens up new, interesting routes of spin-wave amplification and manipulation. In this Review, we will give an overview over the recent developments and achievements in this field.