A primer on equidistribution and pair correlations

This is a survey talk, covering the history and some classical results in the theory of uniform distribution modulo one and Poissonian gap statistics. Topics that are touched upon include: Weyl criterion, metric number theory, discrepancy, pseudo-randomness, Montgomery's conjecture, the Berry-Tabor conjecture, and gap statistics other than pair correlations. The talk concludes with an exposition of many open problems.