Spin waves (SWs) are collective excitations of spins in magnetically ordered materials. The quantized form of a SW is known as a magnon. SWs excited in ferrimagnetic insulators such as yttrium iron garnet (YIG) can transmit angular momentum over distances up to millimeters and avoid dissipative charge transport. They exhibit frequencies of several GHz, close to and beyond the clock frequencies of the state-of-the-art processors making them attractive candidates for an efficient data processing. Magnonics is a research field that explores the excitation, propagation, detection and manipulation of SWs. Recently, magnetization switching of Ni81Fe19 (permalloy or Py) elements induced by SWs was demonstrated enabling the realization of all SW-based computing devices. In this thesis, we address the SW-assisted magnetization reversal or switching of Py magnetic nanostripes as narrow as 50 nm. We excited propagating and interfering SWs having wavelengths between 7 microns down to 80 nm and studied in detail their interaction with nanomagnetic magnon memory bits (NMMBs). We assessed the ability of various magnon modes propagating in 100 nm-thick-YIG film to reverse arrays of Py nanostripes having widths down to 50 nm placed 25 microns away from the SW excitation antenna using all electrical spin wave spectroscopy. Propagating SWs reduced the critical switching fields of all the nanostripe arrays across the studied combinations of nanostripe widths and periods. Propagating ultrashort SWs having a wavelength of 101 nm reversed nanostripes at a precessional power Pprec of 10.6 nW, which is 6.5 times lower than the Pprec needed in case of 7 micron-long SWs. Secondly, we demonstrated the magnetization reversal of differently shaped 200 nm-wide and 800 nm-long Py NMMBs under SW excitation using magnetic force microscopy and micromagnetic simulations. Elliptical NMMBs reversed their magnetization at 10 dB lower SW excitation power than the rectangular NMMBs. We observed changes in the transmission spectra of short-wavelength plane-wave SWs after propagation over 100 microns beneath an array of over 5000 NMMBs programmed in various magnetic states. Simulations revealed that the reversal of an NMMB proceeded via the creation and propagation of vortices. The simulated switching time by vortex movement was below 4.2 ns. We observed a stochastic nature of the magnetization reversal. It was mainly controlled by the incubation delay before nucleating inhomogeneous spin textures that led to the vortex creation. We estimated that the energy needed to switch several elliptical NMMBs could reach down to 2 fJ considering the SW precessional power from experiments and the switching time obtained from simulations. Our microfocus Brillouin light scattering experiments demonstrated that NMMBs were selectively switched using SW interference. The NMMBs imprinted the SW interference pattern with unswitched NMMBs denoting the expected node positions. Our studies with NMMB switching assisted by SW pulses corroborated the stochasticity observed in the simulations and showed that the SW pulse period and the number of switched NMMBs followed an inverse relation. Lastly, X-ray imaging enabled us to study the microscopic interaction of short-wavelength SWs with NMMBs. We observed large phase delays for SWs propagating underneath the NMMBs leading to interference. Our observations are pivotal in realizing efficient all-magnon-based nanoscale memory devices and neural network.