Information scrambling emerges as a cornerstone in understanding thermalization in most closed quantum systems. In such systems, the initial information, though fully preserved under the unitary evolution, is scrambled from local physical objects into those highly non-local objects. The operator size distribution provides a quantitative description of the information scrambling dynamics. In this talk, I will present two recent works on operator size distribution. In the first work, we derive the full time evolution of the size distribution in large N quantum mechanics using the scramblon effective theory. In the second work, we study the dynamics of operator size in open systems, revealing novel dynamical phase transitions driven by the competition between scrambling and dissipation.