We will discuss typical and non-typical boundary behaviours of holomorphic functions of one or several complex variables, from different points of view. We will mainly focus on the case of several complex variables. For instance, a construction will be presented of a function $f$ holomorphic on a domain $D$ of $\mathbb{C}^n$ such that, given any continuous path $p$ in $D$ terminating at a point of the boundary of $D$, with finite length, the image by $f$ of $p$ is dense in $\mathbb{C}$. It is initially inspired by a construction of Globevnik of a function with a specific boundary behaviour, that allowed him to solve a problem in complex geometry. The main ingredient is the notion of labyrinth. (based on several joint works)