Abstract: Abstract: Arc-analytic geometry is a fairly new branch of real analytic and algebraic geometry, inspired by John Nash's questions about the role of arcs in geometry. It studies the so-called arc-analytic functions and arc symmetric sets. In the algebraic setting, it provides the most satisfactory real counterpart of Zariski topology over an algebraically closed field. In the analytic setting, in contrast, it consists at present mostly of tough open problems. I will give a brief history of the subject with an overview of classical results from the late 80's and the 90's, and discuss both the recent progress and questions. The talk should be accessible to senior math undergrads.