  Let $G$ be a finitely generated group, $A$ a finite set of generators and $K$
a subgroup of $G$. We call the pair $(G,K)$ context-free if the set of all
words over $A$ that reduce in $G$ to an element of $K$ is a context-free
language. When $K$ is trivial, $G$ itself is called context-free; context-free
groups have been classified more than 20 years ago in celebrated work of Muller
and Schupp as the virtually free groups.
  Here, we derive some basic properties of such group pairs. Context-freeness
is independent of the choice of the generating set. It is preserved under
finite index modifications of $G$ and finite index enlargements of $K$. If $G$
is virtually free and $K$ is finitely generated then $(G,K)$ is context-free. A
basic tool is the following: $(G,K)$ is context-free if and only if the
Schreier graph of $(G,K)$ with respect to $A$ is a context-free graph.
