Video harmonization is an important and challenging task that aims to obtain visually realistic composite videos by automatically adjusting the foreground's appearance to harmonize with the background. Inspired by the short-term and long-term gradual adjustment process of manual harmonization, we present a Video Triplet Transformer framework to model three spatio-temporal variation patterns within videos, \ie, short-term spatial as well as long-term global and dynamic, for video-to-video tasks like video harmonization. Specifically, for short-term harmonization, we adjust foreground appearance to consist with background in spatial dimension based on the neighbor frames; for long-term harmonization, we not only explore global appearance variations to enhance temporal consistency but also alleviate motion offset constraints to align similar contextual appearances dynamically. Extensive experiments and ablation studies demonstrate the effectiveness of our method, achieving state-of-the-art performance in video harmonization, video enhancement, and video demoireing tasks. We also propose a temporal consistency metric to better evaluate the harmonized videos. Code is available at https://github.com/zhenglab/VideoTripletTransformer.