In the US, I mainly used www.kayak.com to find airline tickets, mainly because they compare several differention competitors at once.
Sometimes it might be beneficial to go to the airports website that you’re flying to, see which airlines fly in there and then go to those actual flight company websites (i.e. SAS, Northwestern, etc). Sometimes cheaper airlines don’t advertise on specific websites beyond their own.
In Sweden, there’s several websites to book flights (beyond the flight companies own website).
The following allow you to book flights and hotel accommodations:
And then there are other websites to just book airline tickets: