Recent advances in photonic integration have propelled microwave photonic technologies to new heights. The ability to interface hybrid material platforms to enhance light–matter interactions has led to the development of ultra-small and high-bandwidth electro-optic modulators, low-noise frequency synthesizers and chip signal processors with orders-of-magnitude enhanced spectral resolution. On the other hand, the maturity of high-volume semiconductor processing has finally enabled the complete integration of light sources, modulators and detectors in a single microwave photonic processor chip and has ushered the creation of a complex signal processor with multifunctionality and reconfigurability similar to electronic devices. Here, we review these recent advances and discuss the impact of these new frontiers for short- and long-term applications in communications and information processing. We also take a look at the future perspectives at the intersection of integrated microwave photonics and other fields including quantum and neuromorphic photonics.