Frequency-chirped　microwave　waveforms　have　high　pulse　compression　ratio　and　are　widely　used　as　radar　waveforms　to　increase　the　detection　range　and　range　resolution.　In　radar　networks,　the　frequency-chirped　microwave　waveforms　generated　in　center　office　(CO)　need　to　be　transmitted　to　remote　base　stations.　During　fiber　transmission,　the　dispersion　of　long-distance　fiber　may　cause　power　fading　to　the　radar　waveforms　which　restricts　the　signal　frequency,　signal　bandwidth　and　transmission　distance.　In　this　paper,　we　review　our　recent　works　about　photonic　generation　and　anti-dispersion　transmission　of　frequency　chirped　microwave　waveforms.　First,　based　on　polarization　multiplexing　Fourier　mode-locked　optoelectronic　oscillator,　frequency　and　bandwidth　doubling　chirped　microwave　signals　are　generated.　By　adding　a　laser,　the　system　can　also　generate　dual-chirp　signals.　Second,　by　combining　the　generation　and　transmission　of　dual-chirp　microwave　waveforms,　we　proposed　a　photonic　scheme　for　the　generation　and　transmission　of　dual-chirp　microwave　signals　based　on　shifting　the　power　fading　frequency　response　to　compensate　the　fiber　dispersion.　In　order　to　further　improve　the　bandwidth　of　dual-chirp　waveforms　and　the　anti-dispersion　transmission　capability,　we　used　optical　frequency　doubling　and　carrier　frequency　shifting　technology　to　achieve　quadruple-bandwidth　dual-chirp　signal　generation　and　transmission　with　the　elimination　of　power　fading.　Moreover,　an　equivalent　splitting　parabolic　phase　modulation　scheme　was　proposed　to　generate　background-free　dual-chirp　microwave　waveforms,　which　is　independent　of　the　direct　current　bias　points　of　the　modulator　and　the　polarization　states　of　the　system.　The　system　can　eliminate　the　power　fading　induced　by　fiber　dispersion　in　principle,　which　has　good　application　prospects　in　radar　networks.