Can machines discover scientific laws automatically? Despite the prevalence of big data, the process of distilling data into scientific laws has resisted automation. Particularly challenging are situations with small amounts of data that is difficult or expensive to collect. This talk will outline a series of research projects, starting with self-reflecting robotic systems, and ending with machines that can formulate hypotheses, design experiments, and interpret the results, to discover new scientific laws. We will see examples from psychology to cosmology, from classical physics to modern physics, from big science to small science.