Abstract. The study of factorization in integral domains is a very vibrant field of mathematics that has enjoyed a renaissance beginning in the 1990s that continues today. In this talk we will look at some "hands on" factorization for some special cases of "nice" domains. If we impose certain finiteness conditions, one can say many things about the factorization structure of a domain. In particular, we will look at two large families of domains where factorization properties of domains exhibit nice structure: orders in rings of algebraic integers and Cohen-Kaplansky domains (atomic domains with onlyfinitely many irreducibles up to associates). We will discuss some of the nice structure that these types of domains possess and we will give a number of examples to help develop intuition.