Vaughan Jones found unexpected connections between subfactor theory and Richard Thompson's group while attempting to construct conformal field theories (CFT). This led to numerous fruitful applications and among others provided a novel way to construct group actions using categories. I am initiating a program strengthening Jones' visionary work where the Thompson group is replaced by a family of groups that I name "forest-skein groups". These groups are interesting on their own, satisfying exceptional properties and having powerful extra-structures for studying them. They are isotropy subgroup of forest-skein categories: categories of planar diagrams mod out by certain skein relations (just like planar algebras are in Jones' subfactor framework). I will briefly say a word about the story of Jones's discovery and then present forest-skein categories and groups using explicit examples.