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Properties of turbulence in space plasmas above and below the proton gyroscale are very different and different descriptions should be used for the large and the small scales. On scales larger than the proton gyroscale, we can treat the plasmas as conducting fluids and use magnetohydrodynamics (MHD). However, on scales smaller than the proton gyroscale, we cannot use MHD due to various kinetic effects. Electron magnetohydrodynamics (EMHD) is a simple fluid‐like model for small‐scale plasmas. In this paper, we discuss properties of EMHD waves and turbulence. In particular, we focus on inverse cascade in EMHD turbulence. Since EMHD waves are helical and magnetic helicity is a conserved quantity, inverse cascade is expected to be a common phenomenon in EMHD. We first focus on inverse cascade and spectral evolution of completely imbalanced EMHD wave packets, in which all waves are moving in the same direction. Then, we discuss inverse cascade and spectral evolution of driven imbalanced EMHD turbulence. We also discuss “pinning” of energy spectra in imbalanced EMHD turbulence.

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