It is the third-highest ranking suit in Contract bridge.
In the "Omnibus" variety of Hearts, the Jack of Diamonds provides a bonus of -10 points to the player taking it in a trick. In this, Omnibus Hearts departs from being a simple trick-evasion game.
The 3 of Diamonds is the opening lead in Ambition, and Diamonds are a "small-money" suit in that game, containing 17 of each round's 85 points.