  Understanding the growth of quasicrystals poses a challenging problem, not
the least because the quasiperiodic order present in idealized mathematical
models of quasicrystals prohibit simple local growth algorithms. This can only
be circumvented by allowing for some degree of disorder, which of course is
always present in real quasicrystalline samples. In this review, we give an
overview of the present state of theoretical research, addressing the problems,
the different approaches and the results obtained so far.
