Abstract: CompactLight is a Design Study funded by the European Union under the Horizon 2020 research and innovation funding programme, with Grant Agreement No. 777431. CompactLight was conducted by an International Collaboration of 23 international laboratories and academic institutions, three private companies, and five third parties. The project, which started in January 2018 with a duration of 48 months, aimed to design an innovative, compact, and cost-effective hard X-ray FEL facility complemented by a soft X-ray source to pave the road for future compact accelerator-based facilities. The result is an accelerator that can be operated at up to 1 kHz pulse repetition rate, beyond today's state of the art, using the latest concepts for high brightness electron photoinjectors, very high gradient accelerating structures in X-band, and novel short-period undulators. In this report, we summarize the main deliverable of the project: the CompactLight Conceptual Design Report, which overviews the current status of the design and addresses the main technological challenges.