The website downdetector.co.uk showed a map of the worst-affected areas, including the UK and much of the US.
A number of problems were also reported in the US, particularly on the east coast around New York.
Many Instagram users took to other social media sites when problems appeared just before 11pm Thursday.
One Twitter user wrote: “What’s going on with Instagram everyone’s saying theirs isn’t loading.”
The hashtag “#instagramdown” quickly became one of the top Twitter trends in the UK and other parts of the world.
Those trying to use the desktop site saw a Facebook logo and a message saying: “Sorry, something went wrong”.
By 11.40pm, 57,000 people around the world had reported issues with the site.
Shortly afterwards, Instagram finally acknowledged the problem.
“We’re working quickly to fix the issue.”
Just after midnight, users reported the site was working again.
Instagram later tweeted an update, writing: “We are now fully recovered and apologise for the disruption!”