Fetoscopy laser photocoagulation is a widely adopted procedure for treating Twin-to-Twin Transfusion Syndrome (TTTS). The procedure involves photocoagulation pathological anastomoses to regulate blood exchange among twins. The procedure is particularly challenging due to the limited field of view, poor manoeuvrability of the fetoscope, poor visibility, and variability in illumination. These challenges may lead to increased surgery time and incomplete ablation. Computer-assisted intervention (CAI) can provide surgeons with decision support and context awareness by identifying key structures in the scene and expanding the fetoscopic field of view through video mosaicking. Research in this domain has been hampered by the lack of high-quality data to design, develop and test CAI algorithms. Through the Fetoscopic Placental Vessel Segmentation and Registration (FetReg2021) challenge, which was organized as part of the MICCAI2021 Endoscopic Vision challenge, we released the first largescale multicentre TTTS dataset for the development of generalized and robust semantic segmentation and video mosaicking algorithms. For this challenge, we released a dataset of 2060 images, pixel-annotated for vessels, tool, fetus and background classes, from 18 in-vivo TTTS fetoscopy procedures and 18 short video clips. Seven teams participated in this challenge and their model performance was assessed on an unseen test dataset of 658 pixel-annotated images from 6 fetoscopic procedures and 6 short clips. The challenge provided an opportunity for creating generalized solutions for fetoscopic scene understanding and mosaicking. In this paper, we present the findings of the FetReg2021 challenge alongside reporting a detailed literature review for CAI in TTTS fetoscopy. Through this challenge, its analysis and the release of multi-centre fetoscopic data, we provide a benchmark for future research in this field.