  In this article, we focus on the charge degree of freedom in cuprate
superconductors and review theoretical insights into the electronic nematic
order, bond-charge orders, and plasmons. The low-energy charge dynamics is
controlled by the spin-spin interaction J, which generates various bond-charge
ordering tendencies including the electronic nematic order. The nematic order
is driven by a d-wave Pomeranchuk instability and is pronounced in the
underdoped region as well as around van Hove filling in the hole-doped case;
the nematic tendency is weak in the electron-doped region. Nematicity
consistent with the d-wave Pomeranchuk instability was reported for hole-doped
cuprates in various experiments. Although the t-J and Hubbard models correctly
predicted the proximity to the nematic instability in cuprates far before the
experimental indications were obtained, full understanding of the charge
ordering tendencies in hole-doped cuprates still requires further theoretical
studies. In electron-doped cuprates, on the other hand, the d-wave bond-charge
excitations around momentum q=(0.5pi,0) explain the resonant x-ray scattering
data very well. Plasmon excitations are also present and the agreement between
the large-N theory of the t-J model and resonant inelastic x-ray scattering
measurements is nearly quantitative in both hole- and electron-doped cuprates.
Theoretically the charge dynamics in cuprates is summarized as a dual structure
in energy space: the low-energy region scaled by J, where the nematic and
various bond-charge orders are relevant, and the high-energy region typically
larger than J, where plasmons are predominant.
