Glaucoma is a chronic neuro-degenerative condition that is one of the world's leading causes of irreversible but preventable blindness. The blindness is generally caused by the lack of timely detection and treatment. Early screening is thus essential for early treatment to preserve vision and maintain life quality. Colour fundus photography and Optical Coherence Tomography (OCT) are the two most cost-effective tools for glaucoma screening. Both imaging modalities have prominent biomarkers to indicate glaucoma suspects, such as the vertical cup-to-disc ratio (vCDR) on fundus images and retinal nerve fiber layer (RNFL) thickness on OCT volume. In clinical practice, it is often recommended to take both of the screenings for a more accurate and reliable diagnosis. However, although numerous algorithms are proposed based on fundus images or OCT volumes for the automated glaucoma detection, there are few methods that leverage both of the modalities to achieve the target. To fulfil the research gap, we set up the Glaucoma grAding from Multi-Modality imAges (GAMMA) Challenge to encourage the development of fundus & OCT-based glaucoma grading. The primary task of the challenge is to grade glaucoma from both the 2D fundus images and 3D OCT scanning volumes. As part of GAMMA, we have publicly released a glaucoma annotated dataset with both 2D fundus colour photography and 3D OCT volumes, which is the first multi-modality dataset for machine learning based glaucoma grading. In addition, an evaluation framework is also established to evaluate the performance of the submitted methods. During the challenge, 1272 results were submitted, and finally, ten best performing teams were selected for the final stage. We analyse their results and summarize their methods in the paper. Since all the teams submitted their source code in the challenge, we conducted a detailed ablation study to verify the effectiveness of the particular modules proposed. Finally, we identify the proposed techniques and strategies that could be of practical value for the clinical diagnosis of glaucoma. As the first in-depth study of fundus & OCT multi-modality glaucoma grading, we believe the GAMMA Challenge will serve as an essential guideline and benchmark for future research.