Integrated Microwave photonics (IMWP) signal processing using Photonic Integrated Circuits (PICs) has attracted a great deal of attention in recent years as an enabling technology for a number of functionalities not attainable by purely microwave solutions. In this context, integrated waveguide Bragg grating (WBG) devices constitute a particularly attractive approach thanks to their compactness and flexibility in producing arbitrarily defined amplitude and phase responses, by directly acting on coupling coefficient and perturbations of the grating profile. In this article, we review recent advances in the field of integrated WBGs applied to MWP, analyzing the advantages leveraged by an integrated realization. We provide a perspective on the exciting possibilities offered by the silicon photonics platform in the field of MWP, potentially enabling integration of highly-complex active and passive functionalities with high yield on a single chip, with a particular focus on the use of WBGs as basic building blocks for linear filtering operations. We demonstrate the versatility of WBG-based devices by proposing and experimentally demonstrating a novel, continuously-tunable, integrated true-time-delay (TTD) line based on a very simple dual phase-shifted WBG (DPS-WBG).