  Quantum random sampling is the leading proposal for demonstrating a
computational advantage of quantum computers over classical computers.
Recently, first large-scale implementations of quantum random sampling have
arguably surpassed the boundary of what can be simulated on existing classical
hardware. In this article, we comprehensively review the theoretical
underpinning of quantum random sampling in terms of computational complexity
and verifiability, as well as the practical aspects of its experimental
implementation using superconducting and photonic devices and its classical
simulation. We discuss in detail open questions in the field and provide
perspectives for the road ahead, including potential applications of quantum
random sampling.
