Viewing fundamental physics processes through the lenses of quantum information storage and processing is a new frontier in gravity and quantum field theory. Much of what we have learnt in the past decade builds on the notion of entanglement and its entropy. The latter quantifies how hard it is to store a quantum-many body state of interest on a classical computer. Complexity is a new player in the high-energy physics context and quantifies how hard it is to prepare a quantum-many body state using limited resources. Learning from the success story of entanglement entropy, establishing universal results on complexity in two-dimensional conformal field theories should open many new research directions, including finding a precise gravity dual. I will discuss recent progress on this problem reported in 2005.02415 and 2007.11555 with Flory.