Counting subgroups of the groups ${\mathbb{Z}}_{n_1}\times \cdots \times {\mathbb{Z}}_{n_k}$: a survey

We present a survey of exact and asymptotic formulas on the number of cyclic subgroups and total number of subgroups of the groups ${\mathbb{Z}}_{n_1}\times \cdots \times {\mathbb{Z}}_{n_k}$, where $k\ge 2$ and $n_1,\dots ,n_k$ are arbitrary positive integers.