In recent years, substantial progresses has been made in understanding and proving a number of energy conditions in quantum field theories (QFTs), which played very important roles for constraining quantum corrections to black hole dynamics in general relativity. In this talk, I will discuss proof of the quantum null energy condition (QNEC), both in holographic CFTs based on AdS/CFT, and in generic CFTs using techniques related to the entanglement structure. Furthermore, I will discuss the connection between the two approaches, and in doing this, deep relations between boundary modular flow and bulk RT surface dynamics will be revealed.