This paper introduces a novel dataset for video enhancement and studies the state-of-the-art methods of the NTIRE 2021 challenge on quality enhancement of compressed video. The challenge is the first NTIRE challenge in this direction, with three competitions, hundreds of participants and tens of proposed solutions. Our newly collected Large-scale Diverse Video (LDV) dataset is employed in the challenge. In our study, we analyze the proposed methods of the challenge and several methods in previous works on the proposed LDV dataset. We find that the NTIRE 2021 challenge advances the state-of-the-art of quality enhancement on compressed video. The proposed LDV dataset is publicly available at the homepage of the challenge: https://github.com/RenYang-home/NTIRE21_VEnh