In-loop filters have been comprehensively explored during the development of video coding standards due to their remarkable noise-reduction capability. In the early stage of video coding, in-loop filters, such as Deblocking Filter, Sample Adaptive Offset, and Adaptive Loop Filter, were performed separately for each component. Recently, cross-component filters were studied to improve the chroma fidelity by exploiting correlations between the luma and chroma channels. This paper summarizes the cross-component filters used in the state-of-the-art video coding standard. Specifically, it includes 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. In this paper, we introduce the origin, development, and status of cross-component filters in the current video coding standards. Finally, we had some discussions on the further evolutions of cross-component filters.