High harmonic generation (HHG) from solids driven by ultra-short and ultraintense laser pulses is attracting more and more attention. Arising from the sub-optical-cycle electron motion, this HHG provides a new perspective for studying high-order nonlinear interactions between light and solids on a very short time scale. Compared with atoms and molecules, the lattice structure of solids possesses translation symmetry, so that HHG from solids will exhibit unique properties. In contrast to bulk media, the distinct electro-optical properties in two-dimensional (2D) materials can give rise to new high harmonic spectral characteristics. This paper summarizes recent studies on HHG from several typical 2D materials and in lightwave electronics.