Abstract: Given a sequence of two or more types of symbols, a run is defined as a succession of–one or more–
identical symbols which are followed and preceded by a different symbol (or by no symbol at all). Runs tests are
based on the length of the longest run or on the total number of runs. They figure among the oldest nonparametric
procedures, and can be used in various setups. We review the different definitions of runs, their development over the
last one hundred years, describe the domains of application of runs tests, and discuss their extension to the multivariate
case.