  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 %.
