Lennuabi is a flight compensation service based in Tallinn, Estonia, run by Lennuabi OÜ and handling claims since 2017. If a flight you took was badly delayed, canceled or overbooked, or you missed a connection, you fill in a short online form and Lennuabi takes the claim to the airline for you. It says more than 35,000 passengers have been compensated so far.
For US travelers, the rules that matter are Europe's. EU Regulation 261/2004 covers any flight leaving an airport in the European Union, whichever airline flies it, and flights into the EU on a European airline. That means a delayed American, Delta or United departure from Paris, Madrid or Frankfurt can qualify, as can a Lufthansa or Air France flight from New York. A US airline's flight from the US to Europe isn't covered. Lennuabi has guides for US carriers including American, Delta, United, Alaska, Frontier and Allegiant, and compensation runs from €250 to €600 per passenger depending on distance, with most transatlantic routes in the €600 band. Payouts are quoted in euros.
There's nothing to pay up front, but the fee is high: the standard charge is 39.7% of any compensation won, rising to 50% if the case goes to court. You can claim from the airline yourself for free, so the service suits people who'd rather not chase the airline, or whose claim has already been turned down.