In this presentation we provide an overview of recent efforts towards developing computing systems based on Spin Waves (SW) instead of charges and voltages. Note that SW computing constitutes a spintronics subfield, which utilizes magnetic excitations for computation and memory applications. We start with an introduction to magnetic interactions, SW physics, and basic SW computing mechanisms. Subsequently, we review state-of-the-art SW devices, i.e., SW interaction-based Majority gates, SW phase rotation Threshold Logic gates, and SW switch Boolean Logic gates, while discussing the specific challenges ahead when attempting to combine such SW gates to obtain circuits and ultimately computing systems. We consider essential aspects, e.g., gate interconnection, logic levels restoration, gate input-output consistency, and fan-out achievement, and we argue that practically relevant pure SW circuits cannot operate independently and they need to be embedded into conventional Complementary Metal-Oxide-Semiconductor (CMOS) circuit wrappers to obtain complete functional hybrid computing systems. We discuss challenges towards the practical realization of such hybrid SW-CMOS systems and present estimates of their potential performance, which suggest that hybrid SW-CMOS systems exhibit ultralow-power operation and may ultimately outperform conventional CMOS circuits in terms of power-delay-area product. Finally, we take a different perspective on SW physics and demonstrate that by leveraging Gilbert dumping, and otherwise unwanted phenomenon, we can obtain extremely effective convolution, an essential neural networks computation kernel, implementations. We conclude with a brief presentation of the SPIDER project approach (EC contract number 101070417), which is the first ever attempt to experimentally demonstrate the feasibility of hybrid SW-CMOS systems.