As it becomes more and more difficult to miniaturize electronic circuits, the information industry is faced with an existential crisis: soon, it will no longer be possible to significantly expand the computational power of tried-and-trusted electronic technology. It should come as no surprise that both science and industry are frantically searching for a way to avert this impending catastrophe, and are even willing to entertain the notion of abandoning conventional electronics altogether if a more future-proof alternative can be found. One field of research that has this potential is spintronics: the use of intrinsic angular momentum—better known as spin—of electrons to store information. One of the key promises of spintronics is the ability to transport digital information without the need to shuttle around electrons, thereby avoiding the adverse phenomenon of Joule heating. To this end, one may simply perturb the magnetic order of a magnetic material. Doing so generates a spin wave or magnon, in which spin is passed between neighboring electrons while their position remains unchanged. In the subfield of magnonics—the study of magnons—the use of electrically insulating magnetic materials is currently being studied extensively by both experimentalists and theoreticians. In this thesis, I study the theoretical properties of magnons in three different systems involving a magnetic insulator and a heavy metal. In Chapter 4, I investigate whether ferromagnetic magnons can contribute to a phenomenon known as unidirectional spin-Hall magnetoresistance (USMR): a change in magnetoresistence of spintronic systems that occurs when the direction of an electric current is reversed. I predict that such an effect can indeed exist, but will most likely be very small. In Chapter 5, I focus on ballistic transport of magnons in one-dimensional ferromagnetic insulator (FI) chains exhibiting strong aniotropy. The anisotropy causes the magnons to become elliptically polarized, which breaks spin conservation and gives rise to characteristics not seen in systems with circular magnons, one example of which is squeezing: a fundamental asymmetry in quantum noise. The strong anisotropy required to produce significant magnon ellipticity is uncommon in real FIs. In Chapter 6, I therefore extend the work of Chapter 5 to antiferromagnetic spin chains, which bear mathematical semblance to anisotropic ferromagnets, but have ellipticity-producing terms that are intrinsically large. I show that the behavior of these systems depends strongly on the coupling to the antiferromagnet’s different sublattices. Although fairly minimal representations of real systems are developed in this work, they nevertheless have large, mostly unexplored parameter spaces, providing ample opportunity for further research in the near future. In the case of magnonic USMR in particular, recent experimental work by Liu et al. [Phys. Rev. Lett., 127:207206, Nov 2021] provides observations that run counter to our model, suggesting an extension of our work is necessary to capture the full phenomenology. On longer terms, a thorough understanding of the behavior of magnons may lead to pure-spintronic devices featuring low dissipation and extremely high operating frequencies. This, in turn, may revitalize advancement of computer hardware after the expected breakdown of Moore’s law.