The article introduces two complementary datasets intended for the development of data-driven solutions for cranial implant design, which remains to be a time-consuming and laborious task in current clinical routine of cranioplasty. The two datasets, referred to as the SkullBreak and SkullFix in this article, are both adapted from a public head CT collection CQ500 (http://headctstudy.qure.ai/dataset) with CC BY-NC-SA 4.0 license. The SkullBreak contains 114 and 20 complete skulls, each accompanied by five defective skulls and the corresponding cranial implants, for training and evaluation respectively. The SkullFix contains 100 triplets (complete skull, defective skull and the implant) for training and 110 triplets for evaluation. The SkullFix dataset was first used in the MICCAI 2020 AutoImplant Challenge (https://autoimplant.grand-challenge.org/) and the ground truth, i.e., the complete skulls and the implants in the evaluation set are held private by the organizers. The two datasets are not overlapping and differ regarding data selection and synthetic defect creation and each serves as a complement to the other. Besides cranial implant design, the datasets can be used for the evaluation of volumetric shape learning algorithms, such as volumetric shape completion. This article gives a description of the two datasets in detail.