By taking appropriate concrete functions on the complex or real numbers, in this nicely written survey the author shows that free groups and free products of groups occur naturally and explicitly. We just mention two of the results surveyed: \textit{S. A. Adeleke, A. M. W. Glass} and \textit{L. Morley} [J. Lond. Math. Soc., II. Ser. 43, No. 2, 255-268 (1991; Zbl 0745.20001)] showed: If \(0\neq a\in\mathbb{R}\) and \(p>1\) is an odd integer, then the mappings \(t_ a,e_ p: \mathbb{R} \to \mathbb{R}\) given by \(t_ a(x)=x+a\), \(e_ p(x)=x^ p\) generate a free group (with composition as group operation). \textit{A. M. W. Glass, S. McCleary} and \textit{M. Rubin} [Math. Z. 214, 55-66 (1993; Zbl 0792.20002)] showed that if \((\Omega,\leq)\) is any countable highly homogeneous poset, then almost all finitely generated subgroups of the group \(\text{Aut}(\Omega,\leq)\) of all order- automorphisms of \((\Omega,\leq)\) are free. Here ``almost all'' means except for a meagre set with regard to a metric defined naturally on \(\text{Aut}(\Omega,\leq)\).