The SHApe Recovery from Partial textured 3D scans challenge, SHARP 2020, is the first edition of a challenge fostering and benchmarking methods for recovering complete textured 3D scans from raw incomplete data. SHARP 2020 is organised as a workshop in conjunction with ECCV 2020. There are two complementary challenges, the first one on 3D human scans, and the second one on generic objects. Challenge 1 is further split into two tracks, focusing, first, on large body and clothing regions, and, second, on fine body details. A novel evaluation metric is proposed to quantify jointly the shape reconstruction, the texture reconstruction and the amount of completed data. Additionally, two unique datasets of 3D scans are proposed, to provide raw ground-truth data for the benchmarks. The datasets are released to the scientific community. Moreover, an accompanying custom library of software routines is also released to the scientific community. It allows for processing 3D scans, generating partial data and performing the evaluation. Results of the competition, analysed in comparison to baselines, show the validity of the proposed evaluation metrics, and highlight the challenging aspects of the task and of the datasets. Details on the SHARP 2020 challenge can be found at https://cvi2.uni.lu/sharp2020/.