A chirped microwave waveform with a large time-bandwidth product (TBWP) can find important applications in modern radar systems and microwave imaging systems. Microwave photonics, a field that studies the generation and processing of microwave signals in the optical domain to take advantage of the ultra-wide bandwidth offered by photonics, has been considered an effective solution for high-frequency and large-bandwidth microwave waveform generation. In this paper, an overview on photonic generation of wideband chirped microwave waveforms is provided. Three major methods are discussed including chirped microwave waveform generation based on spectral shaping and frequency-to-time (SS-FTT) mapping, frequency and bandwidth multiplication, and Fourier-domain mode-locking of an optoelectronic oscillator (OEO). The performance of the techniques for chirped microwave waveform generation is studied. Techniques to generate chirped microwave waveforms based on photonic integrated circuits (PICs) are also discussed.INDEX TERMS Microwave photonics, chirped microwave waveform, arbitrary waveform generation, time bandwidth product, optoelectronic oscillator.This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.