Cranial implants are commonly used for surgical repair of craniectomy-induced skull defects. These implants are usually generated offline and may require days to weeks to be available. An automated implant design process combined with onsite manufacturing facilities can guarantee immediate implant availability and avoid secondary intervention. To address this need, the AutoImplant II challenge was organized in conjunction with MICCAI 2021, catering for the unmet clinical and computational requirements of automatic cranial implant design. The first edition of AutoImplant (AutoImplant I, 2020) demonstrated the general capabilities and effectiveness of data-driven approaches, including deep learning, for a skull shape completion task on synthetic defects. The second AutoImplant challenge (i.e., AutoImplant II, 2021) built upon the first by adding real clinical craniectomy cases as well as additional synthetic imaging data. The AutoImplant II challenge consisted of three tracks. Tracks 1 and 3 used skull images with synthetic defects to evaluate the ability of submitted approaches to generate implants that recreate the original skull shape. Track 3 consisted of the data from the first challenge (i.e., 100 cases for training, and 110 for evaluation), and Track 1 provided 570 training and 100 validation cases aimed at evaluating skull shape completion algorithms at diverse defect patterns. Track 2 also made progress over the first challenge by providing 11 clinically defective skulls and evaluating the submitted implant designs on these clinical cases. The submitted designs were evaluated quantitatively against imaging data from post-craniectomy as well as by an experienced neurosurgeon. Submissions to these challenge tasks made substantial progress in addressing issues such as generalizability, computational efficiency, data augmentation, and implant refinement. This paper serves as a comprehensive summary and comparison of the submissions to the AutoImplant II challenge. Codes and models are available at https://github.com/Jianningli/Autoimplant_II.