There is a notion of flexibility, which acts as a touchstone in a large number of geometric contexts. Originally framed by Gromov as the h-principle, the topic has expanded broadly to influence many fields. The talk will discuss flexibility in symplectic geometry, Stein geometry, and contact geometry, and how the notions of flexibility inter-relate between them. A particular interest here are the flexible/rigid dichotomies we see in these geometries, which has seen rapid progress in recent years. The talk will discuss the general notions and framework, and give a broad tour of recent developments.