The accepted line of the Vienna Gambit is a popular opening and can be traced all the way back to the 19th century, used by top players like Wilhelm Steinitz and Emanuel Lasker.

In the 4. d4 (Steinitz Gambit), White takes the center at the expense of losing the ability to castle, allowing Black to attack White's king.

In the 4. Nf3 (Knight Variation) White prevents Qh4+. If 4. ... g5 (most critical) White undermines with 5. g3, leading to an unclear position.

Objectively, 4. Nf3 is the only move that maintains relative equality with best play.

For explanation of theory tables, see theory table and for notation, see algebraic notation..

1. e4 e5 2. Nc3 Nc6 3. f4 exf4

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Wikipedia has related information at Vienna Game