Charge density wave (CDW) have triggered extensive research in low dimensional systems. The discoveries of CDW provide crucial new clues for understanding intrinsic mechanisms of low dimensional electron-phonon coupling and electron correlation. In addition, the physical properties of low dimensional materials such as magnetism and superconductivity can be fine-tuned with accurately and effectively controlled CDW phase. At the beginning, the briefly introduction of the basic properties of CDW in one-dimensional and quasi one-dimensional materials reveals the physical proprieties of the CDW, for instance, the excite state and the manipulation technologies. Then, focusing on the CDW in two-dimensional system, we mainly introduce the recent research progress and the generation mechanism of CDW in two-dimensional materials. The interaction between CDW and Mott insulators, superconductivity and other orders such as spin density wave and pair density wave provides a new perspective to research the multi-electron collective excitation and electron interaction. The manipulation of multi-electron collective excitation and electron-phonon interaction in CDW though doping, high pressure and laser pulse is also introduced and share a basic similarity to the one-dimensional system. Finally, this article proposed the potential research application of two dimensional CDW.