Unconventional superconductivity often emerges in proximity to various competing or coexisting states. In cuprate superconductors, these states include spin order, charge order, the pseudogap state, and the strange metal phase. A comprehensive understanding of their relationship is fundamental to establishing the mechanism of high-temperature superconductivity. While spin dynamics in cuprates has been extensively investigated using inelastic neutron scattering, charge correlations remain much less understood. The recent advancement of resonant X-ray scattering (RXS) has enabled the detection of charge correlations with unprecedented sensitivity. A series of RXS studies have revealed the universal existence of charge correlations in cuprate materials, which extend across a wide range of the phase diagram. Resonant inelastic X-ray scattering (RIXS) experiments further unveiled the dynamical behaviors of charge order. These findings highlight the important influence of charge correlations on the properties of cuprates. In this article, we review the latest progress in the study of charge order in cuprates using RXS, with a particular emphasis on RIXS experiments. Our focus includes recent works on dynamical charge correlations at high temperature, and uniaxial strain tuning of charge order. We discuss topics including the underlying interactions, microscopic structure and symmetry, and possible influence of charge order on both the superconducting and normal states.