  For the first time, Swift is giving us the opportunity to study supergiant
fast X-ray transients (SFXTs) throughout all phases of their life: outbursts,
intermediate level, and quiescence. We present our intense monitoring of four
SFXTs, observed 2-3 times per week since October 2007. We find that,
unexpectedly, SFXTs spend most of their time in an intermediate level of
accretion ($L_{X}\sim 10^{33-34} $ erg s$^{-1}$), characterized by rich flaring
activity. We present an overview of our investigation on SFXTs with Swift, the
key results of our Project. We highlight the unique contribution Swift is
giving to this field, both in terms of outburst observations and through a
systematic monitoring.
