  An integral domain is atomic if every nonzero nonunit factors into
irreducibles. Let $R$ be an integral domain. We say that $R$ is a bounded
factorization domain if it is atomic and for every nonzero nonunit $x \in R$,
there is a positive integer $N$ such that for any factorization $x = a_1 \cdots
a_n$ of $x$ into irreducibles $a_1, \dots, a_n$ in $R$, the inequality $n \le
N$ holds. In addition, we say that $R$ is a finite factorization domain if it
is atomic and every nonzero nonunit in $R$ factors into irreducibles in only
finitely many ways (up to order and associates). The notions of bounded and
finite factorization domains were introduced by D. D. Anderson, D. F. Anderson,
and M. Zafrullah in their systematic study of factorization in atomic integral
domains. Here we provide a survey of some of the most relevant results on
bounded and finite factorization domains.
