Wildcard-specs

[VERACSD at usc-isi.arpa]

Does UNIX support recursive directory-level matching?  i. e. Does it allow one
to wildcard-specify all files in a dir as well as all files in the dir's
subdirectories?  cf. the use of "**" in Symbolics' pathnames.  

If it does, how does one specify this? (Else, why not?.)

(Context this ? arose in:  I'm (obviously) learning Unix, and want to grep
all files in a dir's hierarchy.)

Thanks.

-- ck