Microwave photonics (MWPs) uses the strength of photonic techniques to generate, process, control, and distribute microwave signals, combining the advantages of microwaves and photonics. As one of the main topics of MWP, radio-over-fiber (RoF) links can provide features that are very difficult or even impossible to achieve with traditional technologies. Meanwhile, a considerable number of signal-processing subsystems have been carried out in the field of MWP as they are instrumental for the implementation of many functionalities. However, there are still several challenges in strengthening the performance of the technology to support systems and applications with more complex structures, multiple functionality, larger bandwidth, and larger processing capability. In this paper, we identify some of the notable challenges in MWP and review our recent work. Applications and future direction of research are also discussed.