Supergiant fast X-ray transients (SFXTs) are a class of high-mass X-ray binaries with possible counterparts in the high energy gamma rays. The Swift SFXT Project1 has conducted a systematic investigation of the properties of SFTXs on timescales ranging from minutes to years and in several intensity states (from bright flares, to intermediate intensity states, and down to almost quiescence). We also performed broad-band spectroscopy of outbursts, and intensity-selected spectroscopy outside of outbursts. We demonstrated that while the brightest phase of the outburst only lasts a few hours, further activity is observed at lower fluxes for a remarkably longer time, up to weeks. Furthermore, we assessed the fraction of the time these sources spend in each phase, and their duty cycle of inactivity. We present the most recent results from our investigation. The spectroscopic and, most importantly, timing properties of SFXTs we have uncovered with Swift will serve as a guide in search for the high energy emission from these enigmatic objects.