  Zero-difference balanced (ZDB) functions integrate a number of subjects in
combinatorics and algebra, and have many applications in coding theory,
cryptography and communications engineering. In this paper, three new families
of ZDB functions are presented. The first construction, inspired by the recent
work \cite{Cai13}, gives ZDB functions defined on the abelian groups $(\gf(q_1)
\times \cdots \times \gf(q_k), +)$ with new and flexible parameters. The other
two constructions are based on $2$-cyclotomic cosets and yield ZDB functions on
$\Z_n$ with new parameters. The parameters of optimal constant composition
codes, optimal and perfect difference systems of sets obtained from these new
families of ZDB functions are also summarized.
