Other special cases include a tailwind, where the plane and wind are acting in the same direction. As you may suspect, the speed of the aircraft increases when there is a tailwind and decreases when there is a headwind.
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That flight set a record for the fastest subsonic transatlantic commercial airline flight — 5 hours and 13 minutes, thanks to a 202 mph tailwind. For reference, the speed of sound is 760 mph; but the plane did not break the sound barrier.
If you are already in the air, going to another airport to land may be the better option. There are many reasons to avoid a takeoff or landing with a tailwind. These range from the fact that takeoff and landing distance requirements will be longer to reduced climb gradient due to higher ground speed over distance.
The Boeing 747 Jumbo Jet reached a top speed of 825 miles per hour which was boosted by a strong jet-stream and tailwind of over 200 miles per hour. Aircraft that cross the Atlantic between North America and Europe flying eastbound are usually boosted by a tailwind that can shave several hours off their flight time.
A headwind or tailwind does not effect an aircraft's Airspeed, but it does subtract or add to the aircraft's Groundspeed, respectively. And, obviously, a headwind or tailwind increases of decreases the time of travel, the amount of fuel used increases or decreases, respectively.
With this in mind, horizontal winds (also known as “crosswinds”) in excess of 30-35 kts (about 34-40 mph) are generally prohibitive of take-off and landing. As far as how this happens, it depends on where you are in flight.
Pilots can raise the spoilers to decelerate the airplane as it approaches the runway. And even while on the runway, pilots will typically leave the wing spoilers raised. Raised wing spoilers create drag, which essentially slows down the airplane so that it's able to brake more quickly.