  Supergiant Fast X-ray Transients (SFXTs) are one of the most intriguing (and
unexpected) results of the INTEGRAL mission. They are a new class of High Mass
X-ray Binaries involving about 20 sources to date, with 8 firmly identified
SFXTs and many candidates. They are composed by a massive OB supergiant star as
companion donor and a compact object. At least four SFXTs host a neutron star,
because X-ray pulsations have been discovered, while for the others a black
hole cannot be excluded. SFXTs display short X-ray outbursts (compared with
Be/X-ray transients) characterized by fast flares on brief timescales of hours
and large flux variability typically in the range 1,000-100,000. The
INTEGRAL/IBIS sensitivity allowed to catch only the bright flares (peaking at
1E36-1E37erg/s), without persistent or quiescent emission. The investigation of
their properties, in particular the rapid variability time scales of their
flaring activity, will greatly benefit from observations with the Energetic
X-ray Imaging Survey Telescope (EXIST), with the possibility to perform a long
term and continuous as possible monitoring of the hard X-ray sky.
