Quantum complexity is a fundamental concept that measures the difficulty of constructing a quantum state from a reference state and a given set of resources. Initially studied in the context of quantum computation, it has recently proven to be a powerful tool in gravitational physics, especially in quantifying the information processing capacity of black holes. This workshop brought together leading experts in the field to discuss recent progress in defining complexity in theories with infinitely many degrees of freedom, and explored the potential of quantum complexity in shedding light on the emergence of spacetime in holographic theories of quantum gravity.