  This chapter reviews the state of the art in mutually synchronized
spin-torque and spin Hall nano-oscillator (STNO and SHNO) arrays. After briefly
introducing the underlying physics, we discuss different nano-oscillator
implementations and their functional properties with respect to frequency
range, output power, phase noise, and modulation rates. We then introduce the
concepts and the theory of mutual synchronization and discuss the possible
coupling mechanisms in spintronic nano-oscillators, such as dipolar,
electrical, and spin-wave coupling. We review the experimental literature on
mutually synchronized STNOs and SHNOs in one- and two-dimensional arrays and
discuss ways to increase the number of mutually synchronized nano-oscillators.
Finally, the potential for applications ranging from microwave signal
sources/detectors and ultrafast spectrum analyzers to neuromorphic computing
elements and Ising machines is discussed together with the specific electronic
circuitry that has been designed so far to harness this potential.
