In the present article, we review the present status of our understand
ing of the shapes of quasicrystals. Although theoretical efforts exist
to determine the equilibrium shape of quasicrystals, very little expe
rimental information exists. We report some preliminary results of our
work in this direction. On the other hand, beautiful growth shapes of
quasicrystals are reported in the literature. However, only recently
theoretical attention is paid to the. problem of atomistic mechanism o
f growth, In spite of limited studies, comparison of theory and experi
ments reveal a difference in growth behaviour between crystal and quas
icrystal.