Gambits are described as being "offered" to an opponent, and that offer is then said to be either "accepted" or "declined".

In modern chess, the typical response to a moderately sound gambit is to accept the material and give the material back at an advantageous time. For gambits that are less sound, the accepting player is more likely to try to hold on to their extra material. A rule of thumb often found in various primers on chess suggests that a player should get three moves (see tempo) of development for a sacrificed pawn, but it is unclear how useful this general maxim is since the "free moves" part of the compensation is almost never the entirety of what the gambiteer gains. Often, a gambit can be declined with no disadvantage.

A gambit is said to be 'sound' if it is capable of procuring adequate concessions from the opponent. There are three general criteria in which a gambit is often said to be sound:
199 Time gain: the player accepting the gambit must take time to procure the sacrificed material and possibly must use more time to reorganize their pieces after the material is taken.
299 Generation of differential activity: often a player accepting a gambit will decentralize their pieces or pawns and their poorly placed pieces will allow the gambiteer to place their own pieces and pawns on squares that might otherwise have been inaccessible. In addition, bishops and rooks can become more active simply because the loss of pawns often gives rise to open files and diagonals. Former world champion Mikhail Tal once reportedly told Mikhail Botvinnik that he had sacrificed a pawn because it was simply in the way.
399 Generation of positional weaknesses: finally, accepting a gambit may lead to a compromised pawn structure, holes or other positional deficiencies.
An example of a sound gambit is the Scotch Gambit: 1.e4 e5 2.Nf3 Nc6 3.d4 exd4 4.Bc4. Here Black can force White to sacrifice a pawn speculatively with 4...Bb4+, but White gets very good compensation for one pawn after 5.c3 dxc3 6.bxc3, or for two pawns after 6.0-0 inviting 6...cxb2 7.Bxb2, due to the development advantage and attacking chances against the black king. As a result, Black is often advised not to try to hold on to the extra pawn. A more dubious gambit is the so-called Halloween Gambit: 1.e4 e5 2.Nf3 Nc6 3.Nc3 Nf6 4.Nxe5?! Nxe5 5.d4. Here the investment (a knight for just one pawn) is too large for the moderate advantage of having a strong center.

• King's Gambit: 1.e4 e5 2.f4
• Queen's Gambit: 1.d4 d5 2.c4
• Evans Gambit: 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.b4
• Rousseau Gambit: 1.e4 e5 2.Nf3 Nc6 3.Bc4 f5
• Smith–Morra Gambit: 1.e4 c5 2.d4 intending 2...cxd4 3.c3 dxc3 4.Nxc3
• Two Knights Defense: 1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6 4.Ng5 d5 with 5.exd5 Na5 6.Bb5+ c6 7.dxc6 bxc6 likely to follow
• Blackmar–Diemer Gambit (BDG): 1.d4 d5 2.e4 dxe4 3.Nc3 followed by 4.f3
• From's Gambit: 1.f4 e5
• Staunton Gambit: 1.d4 f5 2.e4
• Budapest Gambit: 1.d4 Nf6 2.c4 e5
• Scotch Gambit: 1.e4 e5 2.Nf3 Nc6 3.d4 exd4 4.Bc4
• Latvian Gambit: 1.e4 e5 2.Nf3 f5
• Danish Gambit: 1.e4 e5 2.d4 exd4 3. c3
• Blackburne Shilling Gambit: 1.e4 e5 2.Nf3 Nc6 3.Bc4 Nd4?!
This is not a true gambit by Black, since after 4.Nxe5!? Qg5! Black wins material. White can play a gambit themselves with 5.Bxf7+! Ke7 6.0-0! Qxe5 7.Bxg8 Rxg8 8.c3 Nc6 9.d4, when White's two pawns and rolling pawn center, combined with Black's misplaced king, give White strong compensation for the sacrificed bishop.
• Elephant Gambit: 1.e4 e5 2.Nf3 d5!?
• Englund Gambit: 1.d4 e5?!
• Italian Gambit: 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.d4
• Fried Liver Attack: 1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6 4.Ng5 d5 5.exd5 Nxd5 6.Nxf7 Kxf7
• Albin Countergambit: 1.d4 d5 2.c4 e5
• Benko Gambit: 1.d4 Nf6 2.c4 c5 3.d5 b5
• Milner Barry Gambit: 1.e4 e6 2.d4 d5 3.e5 c5 4.c3 Nc6 5.Nf3 Qb6 6.Bd3 cxd4 7.cxd4 Bd7 8.Nc3 Nxd4 9.Nxd4 Qxd4
• Vienna Gambit: 1.e4 e5 2.Nc3 Nf6 3.f4