In this talk we calculate the entanglement entropy in the presence of a moving mirror in a CFT. We employ the AdS/BCFT construction to describe a gravity dual of moving mirrors. We will show that the time evolution of entanglement entropy for a class of moving mirror, which models an evaporating black hole, follows an ideal page curve. In this gravity dual of this model and also in earlier works on holographic page curves, the end of the world-brane in AdS plays a crucial role. I will also present our recent result on their chaotic spectrum in holographic CFTs.