Moves

1.e4 e5 2.f4 exf4 3.Nf3 g5 4.Bc4 g4 5.0-0

This is the Muzio Gambit, the plan is fairly straight forward, white simply intends to attack the black king, and also sacrifice as much as is necessary (perhaps as much as possible in some games)
So white do intend to play Bxf7+ soon.

Main Line

5.-gxf3 6.Qxf3 Qf6 7.e5 Qxe5 8.Bxf7+ Kxf7 9.d4 Qxd4+ 10.Be3!

And That would be the way it is handled today, there does not seem to be so many alternatives since white sacrificed the knight.

Back in the day it seems 9.d4 Qf5 was more topical, I have no idea why that would be preferred but somehow that seems to have been a popular choice.

Games

Shirov - Lapinski
MacDonell - D'Arblay - MacDonell Gambit
MacDonell - La Bourdonnais - MacDonell Gambit
von Der Lasa - Szen
von Der Lasa - Mayet
Staunton - NN
Cochrane - Staunton Ghulam-Kassim Gambit
Dufresne - Anderssen MacDonell Gambit
Devinck - Kieseritzky MacDonell Gambit

Note that the MacDonell and the Ghulam-Kassim are similar gambits I think mostly it is just a moveorder thing, perhaps the most different is the MacDonell 5.Nc3 (since it is not always there the knight goes in the Muzio), the first game is reasonably modern while the rest is from the romantic era.