Supergiant Fast X-ray Transients are a class of Galactic High Mass X-ray Binaries with supergiant companions. Their extreme transient X-ray flaring activity was unveiled thanks to INTEGRAL/IBIS observations. The SFXTs dynamic range, with X-ray luminosities from 1E32 erg/s to 1E37 erg/s, and long time intervals of low X-ray emission, are puzzling, given that both their donor star properties and their orbital and spin periodicities seem very similar to those displayed by massive binaries with persistent X-ray emission. Clumpy supergiant winds, accretion barriers, orbital geometries and wind anisotropies are often invoked to explain their behavior, but still several open issues remain. A review of the main recent observational results will be outlined, together with a summary of the new scenarios proposed to explain their bright flaring X-ray activity. The main result of a long Suzaku observation of the SFXT IGRJ16479-4514 with the shortest orbital period is also briefly summarized. The observation of the X-ray eclipse in this source allowed us to directly probe the supergiant wind density at the orbital separation, leading to the conclusion that it is too large to justify the low X-ray luminosity. A mechanism reducing the accretion rate onto the compact object is required.