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.