The structural and mechanical stability of quasicrystals are important issues due to their potential for possible applications at high temperatures and stresses. The aim of the present work is, therefore, to review the earlier works on conventional crystalline and quasicrystalline materials and also to report the results and the analysis on the HallPetch and inverse HallPetch like behavior of nanoquasicrystalline Al62.5Cu25Fe12.5 alloys. It was observed that, at large grain sizes, the hardness increases with decreasing grain size, exhibiting the conventional HallPetch relationship, whereas for smaller grains, inverse HallPetch behavior was identied. The inverse Hall Petch behavior in the nanoquasicrystalline phase could be attributed to thermally activated shearing of the grain boundaries, leading to grain boundary sliding in nanostructures of quasicrystalline grains. These results were analyzed based on the dislocation pile-up model as well as the grain boundary shearing models applicable to nanomaterials.