Airports including Gatwick, Washington DC and Paris Charles De Gaulle are said to be among those affected.
Passengers have taken to Twitter saying computer problems have hit numerous airlines.
One wrote: “If your entire system is down at REAGAN airport in DC, does that mean the planes aren’t leaving on time?”
Althea Campbell added that all systems are down at OR Tambo International in Gauteng, South Africa.
And @heykvb wrote: “Looks like @lufthansa’s computer system is down. Hope I can still get home today.”
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Amanda B tweeted that BMWI Airport is facing travel chaos.
She said: “@BWI_Airport @SouthwestAir huge lines to check bags, computer system down. Pack patience.
Gatwick Airport said there had been “do delays”.
A spokesman said: “It’s actually an airline system – but it’s all back up and running as I understand.
“It was the reservation check-in system. It’s back up and running.
“No delays”.
The spokesman added that it is “not an airport issue” but that check-in software has affected a few airlines’ check-in systems.
Twitter user NG Artorias said airline Lufthansa’s computer system is down at Frankfurt airport.