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We provide a comprehensive review of the application of slow and fast light (SFL) techniques to the field of microwave photonics. Basic principles leading to the implementation of phase shifting and true time delay operations which are instrumental in this field are first considered. We then focus on the description of the main results obtained by our groups in the implementation of broadband, full 360 phase shifting using coherent population oscillations in semiconductor waveguides. Next, attention is given to the evaluation of the system impairments implied by these devices when included in analog links. Finally, the main results obtained for several microwave photonic applications such as filtering, arbitrary waveform generation and optoelectronic oscillators (OEOs) are reviewed, and other directions for future research in the field are discussed.