  This paper provides a tutorial overview over recent vigorous efforts to
develop computing systems based on spin waves instead of charges and voltages.
Spin-wave computing can be considered as a subfield of spintronics, which uses
magnetic excitations for computation and memory applications. The tutorial
combines backgrounds in spin-wave and device physics as well as circuit
engineering to create synergies between the physics and electrical engineering
communities to advance the field towards practical spin-wave circuits. After an
introduction to magnetic interactions and spin-wave physics, all relevant basic
aspects of spin-wave computing and individual spin-wave devices are reviewed.
The focus is on spin-wave majority gates as they are the most prominently
pursued device concept. Subsequently, we discuss the current status and the
challenges to combine spin-wave gates and obtain circuits and ultimately
computing systems, considering essential aspects such as gate interconnection,
logic level restoration, input-output consistency, and fan-out achievement. We
argue that spin-wave circuits need to be embedded in conventional CMOS circuits
to obtain complete functional hybrid computing systems. The state of the art of
benchmarking such hybrid spin-wave--CMOS systems is reviewed and the current
challenges to realize such systems are discussed. The benchmark indicates that
hybrid spin-wave--CMOS systems promise ultralow-power operation and may
ultimately outperform conventional CMOS circuits in terms of the
power-delay-area product. Current challenges to achieve this goal include
low-power signal restoration in spin-wave circuits as well as efficient
spin-wave transducers.
