The paper surveys automated scientific discovery, from equation discovery and symbolic regression to autonomous discovery systems and agents. It discusses the individual approaches from a "big picture" perspective and in context, but also discusses open issues and recent topics like the various roles of deep neural networks in this area, aiding in the discovery of human-interpretable knowledge. Further, we will present closed-loop scientific discovery systems, starting with the pioneering work on the Adam system up to current efforts in fields from material science to astronomy. Finally, we will elaborate on autonomy from a machine learning perspective, but also in analogy to the autonomy levels in autonomous driving. The maximal level, level five, is defined to require no human intervention at all in the production of scientific knowledge. Achieving this is one step towards solving the Nobel Turing Grand Challenge to develop AI Scientists: AI systems capable of making Nobel-quality scientific discoveries highly autonomously at a level comparable, and possibly superior, to the best human scientists by 2050.