Geometrically frustrated lanthanide gallium garnets find practical applications as low temperature magnetocalorics, but the competing interactions in these materials may give also rise to exotic magnetic states. The main focus of recent studies has been Gd3Ga5O12 (GGG). Here we discuss Dy3Ga5O12 (DyGG) and Ho3Ga5O12 (HoGG),which have substantial single ion anisotropy, and are candidates for exhibiting novel quantum magnetism. DyGG is reported to have a long range ordered (LRO) transition at 0.373 K and a short-range ordered (SRO) state at 0.6 - 0.7 K, while for HoGG, SRO and LRO are reported to coexist below 0.3 K. The nature of the magnetic ordering and magnetic interactions has not been reported. Neutron experiments on powder samples of DyGG ( isotopically enriched) and HoGG down to 50 mK are proposed to determine the magnetic ground states and dominant magnetic interactions.