Experiment design is hallmark of virtually all research disciplines. In many settings, one important challenge is how to automatically design experiments over large action/design spaces. Furthermore, it is also important for such a procedure to be adaptive, i.e., to adapt to the outcomes of previous experiments. In this talk, I will describe recent progress in using data-driven algorithmic techniques for adaptive experiment design, also known as active learning and Bayesian optimization in the machine learning community. Building upon the Gaussian process (GP) framework, I will describe case studies in personalized clinical therapy and nanophotonic structure design. Motivated by these applications, I will show how to incorporate real-world considerations such as safety, preference elicitation, and multi-fidelity experiment design into the GP framework, with new algorithms, theoretical guarantees, and empirical validation. Time permitting, I will also briefly overview a few other case studies as well.