Taking Grep to a Lower Level

> The general question is:
>
> * How can 'grep' be asked to work like 'ls -R' -- i.e., to search
> in all files in the current directory, and all directories under it?

Ahhh! I think we've seen 2 answers -- 
1) With old version of grep use    find | grep or find -exec grep 
2) With newer versions of grep use grep -r