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In 1935 J.G. van der Corput introduced a sequence which has excellent uniformdistribution properties modulo 1. This sequence is based on a very simpledigital construction scheme with respect to the binary digit expansion.Nowadays the van der Corput sequence, as it was named later, is the prototypeof many uniformly distributed sequences, also in the multi-dimensional case.Such sequences are required as sample nodes in quasi-Monte Carlo algorithms,which are deterministic variants of Monte Carlo rules for numericalintegration. Since its introduction many people have studied the van der Corputsequence and generalizations thereof. This led to a huge number of results.  On the occasion of the 125th birthday of J.G. van der Corput we survey manyinteresting results on van der Corput sequences and their generalizations. Inthis way we move from van der Corput's ideas to the most modern constructionsof sequences for quasi-Monte Carlo rules, such as, e.g., generalized Haltonsequences or Niederreiter's $(t,s)$-sequences.

From van der Corput to modern constructions of sequences for quasi-Monte Carlo rules