This talk can be seen as the second part of the one given by Luis Paris last February. To make the exposition self-contained, I will start with the definition (and the motivation) of this new family of groups and therefore I will present some results (and questions) on pure subgroups and crystallographic quotients of virtual Artin groups. At the end, if time permits, I will present other families of groups that admit similar notions of virtual extension. Joint work with Luis Paris and Anne Laure Thiel.