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Among the prospects of new solid state laser-materials the garnet-like structure hosts have a privileged place due to good chemical, thermal and optical properties respectively. The oxyde compounds with usual general formula C3A2D3O12 show three sites inside the cubic structure: C is the dodecahedral site A the octahedral site and D is the tetrahedral site. So that easy substitutions with either rare-earth ions (Ce3+, Ne+, Er3+, Tm3+, He+) in the dodecahedral site or metal transition ions (Cr3+) in the octahedral site may be done with high concentrations and rods may be grown by the standard Czochralski method technique. The most known singlecrystal is Y3A15O12:Nd3+(YAG) which is, to day, the reference of Nef-doped solid state laser materials emitting an emission line at 1064nm. But a new one Gd3Sc2Ga3O12:Cr3+-Nd3+(GSGG) which has recently shown better laser performances, could be commercialized in the future due to an efficient Cr3+-Nd3+ energy transfer process under visible broad band Xe-flash lamps pumping [1-2-3]. Unfortunately, this crystal contains expensive and rare Sc3+cations and then another approach has been tested to replace SO+ cations by more common ions as for example Ga3+ions (Gd3Ga5O12)(GGG) or Al3+ions (Gd3Al2Ga3012) or also Ca2+, mg2+ and Zr44- cations in substituted GGG (Ca2+, mg2+, Zr4+ ) with formula Gd3-xCaxGas-x-2yMgyZrx+yO12 [4-5-6-7]. This paper summarizes our own approach in the search on such oxyde garnet-like structure laser materials, restricting the results with Nd3+ activator ions and codoped by Cr3+ or Ce3+ sensitizer ions and we also give the trends of this class of solid state laser materials
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