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.
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 Cool Breeze's reply was promoted to an answer.
CB, Thanks for spotting my error.

Of course the plural possessive is Smiths'