Appears in collection : Mathematics Inspired by Physics

We will present an approach to the construction of actions of braid groups on triangulated categories arising in the (additive) categorification of cluster algebras and varieties. The examples will be inspired by combinatorial braid group actions constructed by Fraser, Fock-Goncharov, Goncharov-Shen and others. The results we will present were obtained in several joint projects notably involving, in chronological order, Chris Fraser, Yilin Wu, Alessandro Contu, Miantao Liu, Haoyu Wang and Xiaofa Chen.