|Abstract. The detection of millisecond-duration Fast Radio Bursts (FRBs) at apparently cosmological distances has opened up new possibilities of probing the Intergalactic Medium. The dispersion measures of FRBs will enable us to detect the "missing" baryons in the low-redshift Universe that constitute >50% of the baryonic mass at z~0. Several FRBs exhibit evidence of temporal smearing by turbulence that must reside at cosmological distances. I will discuss the likely ambient properties of the plasma, the location of this turbulence, and present several arguments why the bulk of the dispersion measure does not emanate from regions near the bursts themselves, thus ruling out some suggestions as to their origin. I will also provide a comprehensive explanation for the Galactic latitude dependence of FRBs and use this to measure their logN-logS distribution.