Varieties of group representations

A group representation is a pair $(A,\Gamma)$, where $A$ is a module over a commutative ring $K$ with identity and $\Gamma$ is a group that acts on $A$. In the category of group representations over a fixed $K$, both $A$ and $\Gamma$ are variable. We study varieties in this category. This paper is a survey of results and problems in this area and connections with other topics.