The firm has as many as 25 million customers in the UK, while it also provides services for a range of other brands, including the likes of Sky, Tesco, Giffgaff and Lycamobile, but a problem with a third-party supplier triggered the outage earlier today (06.12.18).
O2 said: "We believe other mobile operators around the world are also affected. Our technical teams are working with their teams to ensure this is fixed as quickly as possible.
"We'd encourage our customers to use wi-fi wherever they can and we apologise for the inconvenience caused."
In September, meanwhile, EE - which is the biggest mobile network in the UK - announced that it will be the first network to provide 5G in the country.
Marc Allera - the CEO of consumer business at BT, which owns EE - said: "Our customers want a fast and reliable 4G connection, and that's what we're working to give them.
"We are using the investment we made in 3G spectrum nearly 15 years ago to give customers today a great experience with the latest smartphones on 4G, and build our foundation for 5G in 2019.
"We're constantly evolving, and the customer experience of 5G will be dictated by the quality of the 4G network underneath."