In this talk, I will review recent progress in defining a universal measure of quantum complexity based on operator growth and state evolution in Krylov space for both unitary and non-unitary dynamics. After introducing Krylov space techniques, I will focus on the complexity measure associated with quantum state evolution, specifically ‘Spread Complexity,’ along with explicit examples and general properties. I will use Spread Complexity to investigate measurement-induced effects on wave function spreading in tight-binding models. Additionally, I will discuss the impact of PT-symmetric phase transitions on wave function dynamics using Spread Complexity. Finally, I will propose a potential connection between classical integrability, quantum chaos, and the topology of phase space flow through the lens of Spread Complexity.