Cognitive radio is considered as a possible disruptive force to improve the spectral resource efficiency through sensing and interacting with the environment. Traditional electrical technologies to implement the cognitive radio face challenges in terms of bandwidth, resolution, and speed. In this paper, the concept and architecture of broadband cognitive radio systems enabled by photonics are proposed. Key microwave photonic techniques for the architecture are reviewed, including the photonics-based spectrum sensing, the photonic arbitrary waveform generation, the photonics-based self-interference cancellation processing, and the microwave photonic dechirp processing and radar imaging. A preliminary demonstration of a cognitive radar system enabled by photonics is performed. The future possible research directions on this topic are discussed.