possible to DELETE CASCADE?

Is it possible for a query to delete a record and all of its
foreign-key dependents?

I see DROP CASCADE, but not a DELETE CASCADE.

What I'm trying to do:
I have a "clients" table.
I have many different tables that use the clients.id as a foreign key.
When I delete a client, I want it to delete all records in those many
different tables that reference this client.

Right now I have my script passing many queries to delete them
individually.  ("delete from history where client_id=?; delete from
payments where client_id=?" -- etc)

Any shortcut way to do this?