  Non-crossing partitions have been a staple in combinatorics for quite some
time. More recently, they have surfaced (sometimes unexpectedly) in various
other contexts from free probability to classifying spaces of braid groups.
Also, analogues of the non-crossing partition lattice have been introduced.
Here, the classical non-crossing partitions are associated to Coxeter and Artin
groups of type $\mathsf{A}_n$, which explains the tight connection to the
symmetric groups and braid groups. We shall outline those developments.
