In-loop filters have been comprehensively explored during the development of video coding standards due to their remarkable noise-reduction capabilities. In the early stage of video coding, in-loop filters, such as the deblocking filter, sample adaptive offset, and adaptive loop filter, were performed separately for each component. Recently, cross-component filters have been studied to improve chroma fidelity by exploiting correlations between the luma and chroma channels. This paper introduces the cross-component filters used in the state-of-the-art video coding standards, including the cross-component adaptive loop filter and cross-component sample adaptive offset. Cross-component filters aim to reduce compression artifacts based on the correlation between different components and provide more accurate pixel reconstruction values. We present their origin, development, and status in the current video coding standards. Finally, we conduct discussions on the further evolution of cross-component filters.