  In recent years, there has been a rising interest in high-dimensional quantum
states and their impact on quantum communication. Indeed, the availability of
an enlarged Hilbert space offers multiple advantages, from larger information
capacity and increased noise resilience, to novel fundamental research
possibilities in quantum physics. Multiple photonic degrees of freedom have
been explored to generate high-dimensional quantum states, both with bulk
optics and integrated photonics. Furthermore, these quantum states have been
propagated through various channels, \textit{e.g.} free-space links,
single-mode, multicore, and multimode fibers and also aquatic channels,
experimentally demonstrating the theoretical advantages over two-dimensional
systems. Here, we review the state of the art on the generation, the
propagation and the detection of high-dimensional quantum states.
