We present an overview of our Supergiant Fast X-ray Transients (SFXT) project, that started in 2007, by highlighting the unique observational contribution Swift is giving to this exciting new field. By means of outburst detection with Swift/BAT and follow-up with Swift/XRT, we demonstrated that while the brightest phase of the outburst only lasts a few hours, further significant activity is observed at lower fluxes for a considerably longer (weeks) time. After intense monitoring with Swift/XRT, we now have a firm estimate of the time SFXTs spend in each phase. The 4 SFXTs we monitored for 1-2 years spend between 3 and 5 % of the time in bright outbursts. The most most probable flux level at which a random observation will find these sources, when detected, is F(2-10 keV) ~ 1-2E-11 erg cm^{-2} s^{-1} (unabsorbed), corresponding to luminosities of a few 10^{33} to a few 10^{34} erg s^{-1}. Finally, the duty-cycle of inactivity ranges between 19 and 55 %.
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