  In the first part of this survey, we present classical notions arising in
combinatorics on words: growth function of a language, complexity function of
an infinite word, pattern avoidance, periodicity and uniform recurrence. Our
presentation tries to set up a unified framework with respect to a given binary
relation.
  In the second part, we mainly focus on abelian equivalence, $k$-abelian
equivalence, combinatorial coefficients and associated relations, Parikh
matrices and $M$-equivalence. In particular, some new refinements of abelian
equivalence are introduced.
