would you write The Smith's or The Smiths?
If the reference is to a specific smith, the smith's, a singular genitive, is possible: Where is the smith's anvil?

If you mean a family whose surname is Smith, the is always used but the plural genitive is formed by placing the apostrophe after the plural s: This is the Smiths' house. Of course no apostrophe is used if the genitive is not required: The Smiths live in this house.

Hi Anon:

It depends. Either of these is OK.

We invited the Smiths for dinner.
We are going to the Smith's for dinner.
Students: Are you brave enough to let our tutors analyse your pronunciation?
 Cool Breeze's reply was promoted to an answer.
CB, Thanks for spotting my error.

Of course the plural possessive is Smiths'