Literature for restrictions that make NPC-Problems to P

The boolean satisfiability problem is in $\mathcal{NPC}$. But if you only get Horn clauses, it is in $\mathcal{P}$.

I've already heard similar statements. Do you know a more general statement when problems in $\mathcal{NPC}$ get to problems in $\mathcal{P}$ because of restrictions?

If something like that does not exist, do you know literature where such restrictions are described?