Diabetic Retinopathy (DR) is the most common cause of avoidable vision loss, predominantly affecting the working-age population across the globe. Screening for DR, coupled with timely consultation and treatment, is a globally trusted policy to avoid vision loss. However, implementation of DR screening programs is challenging due to the scarcity of medical professionals able to screen a growing global diabetic population at risk for DR. Computer-aided disease diagnosis in retinal image analysis could provide a sustainable approach for such large-scale screening effort. The recent scientific advances in computing capacity and machine learning approaches provide an avenue for biomedical scientists to reach this goal. Aiming to advance the state-of-the-art in automatic DR diagnosis, a grand challenge on "Diabetic Retinopathy - Segmentation and Grading" was organized in conjunction with the IEEE International Symposium on Biomedical Imaging (ISBI - 2018). In this paper, we report the set-up and results of this challenge that is primarily based on Indian Diabetic Retinopathy Image Dataset (IDRiD). There were three principal sub-challenges: lesion segmentation, disease severity grading, and localization of retinal landmarks and segmentation. These multiple tasks in this challenge allow to test the generalizability of algorithms, and this is what makes it different from existing ones. It received a positive response from the scientific community with 148 submissions from 495 registrations effectively entered in this challenge. This paper outlines the challenge, its organization, the dataset used, evaluation methods and results of top-performing participating solutions. The top-performing approaches utilized a blend of clinical information, data augmentation, and an ensemble of models. These findings have the potential to enable new developments in retinal image analysis and image-based DR screening in particular.