Data science is labor-intensive and human experts are scarce but heavily involved in every aspect of it. This makes data science time consuming and restricted to experts with the resulting quality heavily dependent on their experience and skills. To make data science more accessible and scalable, we need its democratization. Automated Data Science (AutoDS) is aimed towards that goal and is emerging as an important research and business topic. We introduce and define the AutoDS challenge, followed by a proposal of a general AutoDS framework that covers existing approaches but also provides guidance for the development of new methods. We categorize and review the existing literature from multiple aspects of the problem setup and employed techniques. Then we provide several views on how AI could succeed in automating end-to-end AutoDS. We hope this survey can serve as insightful guideline for the AutoDS field and provide inspiration for future research.