They are all still there. They aren't played much at the higher grandmaster levels, but they can be played anytime and help really spice up the game. Nearly my entire white repertoire consists of gambits with e4.
Romantic Openings - Are they still around today?
#1
The romantic openings have been refuted. Defensive play has become stronger and the sacrificed pawn leads to an endgame loss.

Romantic openings such as the King's Gambit and the Evans Gambit are still around and perfectly playable. Opening theory has come up with equalizing lines so they are no longer the fearsome weapons they were in those thrilling days of yesteryear, but they are certainly dangerous below IM level. Those who choose them as white can often catch their opponent off guard as they are rarely played today.
They rarely appear at titled-player level as those players know the equalizing lines and the unbalanced nature of the positions (material advantage vs initiative and attacking chances) lead to a greater % of wins and losses rather than draws. Top players' defensive abilities make cashing in the attack problematical, making GMs wary of employing them and leading lesser players. seeing the dearth of these games in GM play, to consider them unsound.
Still, they can work. In 1960 (Mar del Plata) Spassky overwhelmed Fischer with a King's Gambit. Fischer wrote an article for American Chess Quarterly detailing his improved plan "refuting" the gambit, but Spassky used it again to beat Bronstein and Karpov. In fact, over his career Spassky won all 16 King's Gambits he played.

Kasparov played some Evans Gambits in the 1990s; if it's good enough for him, it's playable at every level.

the kings gambit and evans gambit have not been refuted by any means not even in the top computer championships. in the kings gambit top players know the lines and white loses the advantage but is never losing in classical. nepo plays it fairly often in blitz and beat firouzja just two months ago
the undeserved bad reputation of the kings gambit has been a great blessing to many players. black never sees it and usually knows only two of three moves while white plays it all the time and knows the plans. i saw some posts by someone that showed that it scores better than the london and as well as the queens gambit. i am trying to learn it now.
as for the evans it has a reputation for being drawn at the top level but it does really well for us
At one point in chess history, a phase of time known as romanticism occured. This era of chess was marked by brutal sacrifices and open games, typically with 1.e4. However, modern chess slowly came in and knocked out romanticism.
How many romantic chess openings still hold ground today?