In this talk, we introduce and explore the concept of entropy flexibility in both discrete-time and continuous-time dynamical systems. This property, which strengthens Katok’s intermediate entropy property, requires that the system’s entropy behaves “continuously” from both the measurable and topological viewpoints. Entropy flexibility suggests a stronger form of Katok’s entropy conjecture. We will present a range of systems that exhibit this property. This is joint work with Alexander Arbieto and Piotr Oprocha.