The theory of irregularities of distribution originated with van der Corput’s questions (1935) about uniform distribution of sequences on the real line. Klaus Roth introduced a new perspective (1954), and started the subject of geometric discrepancy theory, when he related the dynamic problem on the line to a static asymptotic geometric problem in the plane. In this subject, the questions have been attacked in many ways: through combinatorics, harmonic analysis, and probability theory. The flavor of the subject will be illustrated through examples and a few results. No prior experience with this subject will be assumed in this lecture.