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In the first part of the review, I discuss ways of obtainingLorentz-Invariance-Violating (LIV) space-time foam in the modern context ofstring theory, involving brane world scenarios. The foamy structures areprovided by lower-dimensional background brane defects in a D3-brane Universe,whose density is a free parameter to be constrained phenomenologically. Suchconstraining can be provided by high energy gamma-ray photon tests, includingultra-high energy/infrared photon-photon scattering. In the second part, Ianalyze the currently available data from MAGIC and FERMI Telescopes on delayedcosmic photon arrivals in this context. It is understood of course thatconventional Astrophysics source effects, which currently are far from beingunderstood, might be the dominant reason for the observed delayed arrivals. Ialso discuss how the stringent constraints from studies ofsynchrotron-radiation from distant Nebulae, absence of cosmic birefringence andnon observation of ultra-high-energy cosmic photons can be accommodated withinthe aforementioned stringy space-time foam model. I argue that, at least withinthe currently available sets of astrophysical data, the stringy foam model canavoid all theses constraints in a natural range of the string coupling and massscale. The key features are: (i) transparency of the foam to electrons andcharged probes in general, (ii) absence of birefringence effects and (iii) abreakdown of the local effective lagrangian formalism. However, in order toaccommodate, in this theoretical framework, the data of the FERMI satellite onthe delayed arrival of photons from the short intense Gamma Ray Burst GRB090510, in a way consistent with the findings of the MAGIC telescope, a nonuniform density of brane foam defects must be invoked.

String Quantum Gravity, Lorentz-Invariance Violation and Gamma-Ray Astronomy