• ITA Matrix (aggregator, how-to and background)
• Skiplagged (aggregator, also searches for throwaway tickets) prices in USD
• Skyscanner (aggregator)
• Kayak (aggregator, part of Booking Holdings Inc.)
• Google Flights (aggregator)
• Momondo (aggregator, danskt bolag, sköts av Kayak som är en del av Booking Holdings Inc.)
• Expedia (aggregator/OTA) primarily for charter trips, enforces weird booking rules
• CheapOAir (OTA) prices in USD
• Booking.com (aggregator)
• Agoda (aggregator/OTA, part of Booking Holdings Inc.)
• Orbitz (OTA)
• Sembo (OTA, Helsingborg, Stena Line Travel Group AB) [SRF ✔]
• Allaflygbiljetter.se (aggregator)
• Flygresor.se (aggregator, Flightmate AB, part of Etraveli Group AB) [SRF ✔]
• SuperSaver (aggregator, Svenska Resegruppen AB, part of Etraveli Group AB) [SRF ✔]
• Travelstart (aggregator, Svenska Resegruppen AB, part of Etraveli Group AB) [SRF ✔]
• MyTrip (aggregator, Svenska Resegruppen AB, part of Etraveli Group AB) [SRF ✔]
• Seat24 (aggregator, Svenska Resegruppen AB, part of Etraveli Group AB) [SRF ✔]
• Ticket.se (OTA, ägs av Braganza) [SRF ✔]
• Travellink (OTA, ägs av https://edreams.com)
• JetRadar (aggregator) prices in USD/EUR
• Hotwire (OTA) prices in USD
• Travelocity (OTA) priser i USD
• SecretFlying
• BilligaFlygbiljetter.se (aggregator, ägs av Vuelos Baratos Ltd.) unusally poor UX website
• CitizenPlane (a sort of aggregator, not an OTA) ägs av franskt bolag, en société par actions simplifiée. Should probably be avoided.

You can also book tickets directly from many airlines.

Airlines

• Pegasus, Turkish airline, based in Istanbul SAW
• WizzAir, based in Hungary (but their app is horrible, 118 MB, also requests superuser rights?!)

Review articles

https://upgradedpoints.com/best-websites-for-booking-cheap-flights
https://www.frommers.com/slideshows/848046-the-10-best-and-worst-airfare-search-sites
https://www.topfivebuzz.com/20-best-flight-search-engines-for-international-flights-to-find-cheapest-airfares
https://www.forbes.com/sites/johnnyjet/2017/10/04/5-best-online-tools-for-searching-flights

An aggregator is only as good as the OTAs (online travel agencies) it canvasses. There are booking engines that find prices themselves (Expedia, Priceline, Hotwire). And then there are aggregators—sites that do not book tickets but instead search dozens of booking engines, airfare sites, and OTAs and compile the results in one place; you then click through to the one of your choice to make the actual purchase.
https://www.frommers.com/slideshows/848046-the-10-best-and-worst-airfare-search-sites

More links

• Svenska Resebyrå- och arrangörsföreningen (SRF), medlemsförteckning
• SVT artikel om Etraveli Group AB
• Life of an Airline Flight: What Systems Get You From Here to There via the Air, youtube video of talk by Adam Fletcher (2019)