Multi-class segmentation of the aorta in computed tomography angiography (CTA) scans is essential for diagnosing and planning complex endovascular treatments for patients with aortic dissections. However, existing methods reduce aortic segmentation to a binary problem, limiting their ability to measure diameters across different branches and zones. Furthermore, no open-source dataset is currently available to support the development of multi-class aortic segmentation methods. To address this gap, we organized the AortaSeg24 MICCAI Challenge, introducing the first dataset of 100 CTA volumes annotated for 23 clinically relevant aortic branches and zones. This dataset was designed to facilitate both model development and validation. The challenge attracted 121 teams worldwide, with participants leveraging state-of-the-art frameworks such as nnU-Net and exploring novel techniques, including cascaded models, data augmentation strategies, and custom loss functions. We evaluated the submitted algorithms using the Dice Similarity Coefficient (DSC) and Normalized Surface Distance (NSD), highlighting the approaches adopted by the top five performing teams. This paper presents the challenge design, dataset details, evaluation metrics, and an in-depth analysis of the top-performing algorithms. The annotated dataset, evaluation code, and implementations of the leading methods are publicly available to support further research. All resources can be accessed at https://aortaseg24.grand-challenge.org.