  We review the recent advances reported in the field of integrated photonic
waveguide meshes, both from the theoretical as well as from the experimental
point of view. We show how these devices can be programmed to implement both
traditional signal processing structures, such as finite and infinite impulse
response filters, delay lines, beamforming networks as well as more advanced
linear matrix optics functionalities. Experimental results reported both in
Silicon and Silicon Nitride material platforms will be presented. We will also
discuss the main programming algorithms to implement these structures and
discuss their applications either as standalone systems or as part of more
elaborated subsystems in microwave photonics, quantum information and machine
learning
