Airfare

Try www.itasoftware.com, only because it allows you to put very flexible dates and look a month out to see which dates are cheaper than others. Caveat: sometimes the results you see are faulty because the algorithms used can derive some weird combinations of carriers and routing. Most of the time, for uncomplicated queries, the site works just fine but it's not that different from Kayak.

There is no one magic site since the airlines (not the comparison sites) ultimately control the fares - moreover, some airlines are opting out of comparison sites because they want to steer travelers to their own sites. The best thing you can do is track fares early, be very flexible with your schedule, look into budget carriers which may or may not appear on comparison site results, use any airline or credit card points you have, and be open to traveling off season or when there's a sale fare. Consider airlines you may not have used before (or are familiar with): Turkish Air, Air Berlin, WOW Air, etc.

Try Skyscanner. I use Skycanner to search for flights, and then book our flights through specific airline websites.

Bonus: if your travel is somewhat flexible, you can leave the "To" (destination) field empty and see which destinations are cheapest on your preferred dates.

The 'Mileage Run' section at Flyertalk is good at compiling current airfare deals and good pricing. Just note that:

1. Sometimes the really good fares posted there get sold out or pulled by the airlines within hours of them getting posted, so be ready to move quickly if you see something you like

2. If you post that you're looking for a specific route on a specific date there, you will be rather crankily told to use ITA Matrix because that's usually where the posters there are pulling the sale fare data from to begin with.

3. Thread titles are heavy on airline and airline codes, only some of which are easy to google (ex- ME3 means the Middle East 3- Qatar, Ethiad, and Emirates)

If you're willing to deal with Flyertalk's quirks though, they can be a very good resource.

So what is "cheap"? Kayak is just a reporting tool It shows you what is out there.

Actually if you really want cheap you are probably going to have to go to the discount carriers website. Norwegian, Icelandic and WOW are your best bets and those won't be discussed on Flyertalk (Flyertalk focuses on airlines that allow the posters to earn miles, not just get a good deal) Those airlines often aren't on places like Kayak.

The "Good deals" thread on Flyertalk has featured any number of Norwegian and WOW offerings since a lot of people will pounce on a sub-$500 transatlantic fare like that.

I have done a lot of looking over the years and I find in the end the best prices come from the airlines themselves and the bonus is you are directly booked with them and don't have the third party problems if something goes wrong. Some of those discount sights won't let you pick a seat. And I have always felt that no seat assignment no seat! You run a big risk of being the one bumped on an over full flight. You can research on sites like Kyak because you will see which airlines seem to trend lower prices and then go to the airline website and see what you can find. Also make sure you clear "cookies" because they will link you up and know you are shopping around.