In this talk, I will present an overview of recent developments on the non-uniqueness of weak solutions to the incompressible Navier–Stokes equations—a question that lies at the core of mathematical fluid dynamics. I will highlight the main ideas behind these constructions and discuss their implications for the classical notion of determinism in viscous flows. The second part of the talk will focus on the most recent advances achieved through convex integration, which has emerged as a powerful framework for constructing non-unique and pathological solutions.