Treasures in Thieves in Time work somewhat similar to previous entries in the Sly series. They are well hidden in each hub area, and when you find one, press Circle to grab it. Once you do, you will have a time limited to return it to your hideout. Note that taking damage of any kind will destroy the treasure and you will have to do it all over again.
There are a total of 12 treasures to be found in each hub area, with the arcade game in each episode's hideout being unlocked for finding and bringing back all 12 treasures. It is highly recommended that you have at least the Paraglider and Rail Sprint abilities from ThiefNet. Also, you will need all of Sly's costumes, since some treasures are behind doors that only open for certain costumes.