We described a challenge named "Diabetic Retinopathy (DR)-Grading and Image Quality Estimation Challenge" in conjunction with ISBI 2020 to hold three sub-challenges and develop deep learning models for DR image assessment and grading. The scientific community responded positively to the challenge, with 34 submissions from 574 registrations. In the challenge, we provided the DeepDRiD dataset containing 2,000 regular DR images (500 patients) and 256 ultra-widefield images (128 patients), both having DR quality and grading annotations. We discussed details of the top 3 algorithms in each sub-challenges. The weighted kappa for DR grading ranged from 0.93 to 0.82, and the accuracy for image quality evaluation ranged from 0.70 to 0.65. The results showed that image quality assessment can be used as a further target for exploration. We also have released the DeepDRiD dataset on GitHub to help develop automatic systems and improve human judgment in DR screening and diagnosis.