UPDATE 13/03/2015: Rockstar has released a title update for Grand Theft Auto 5 that includes fixes for GTA Online and Story Mode.

Grand Theft Auto 5 title update 1.22 for the PlayStation 3 and Xbox 360, and 1.08 for the PS4 and Xbox One, are in varying stages of release.

It's currently available for PS3 and PS4, and will be coming to Xbox 360 and Xbox One soon, Rockstar said.

Here are the brief patch notes, from Rockstar Support:

Fixes for GTA Online to improve stability, and other minor fixes for both GTA Online and Story Mode.

ORIGINAL STORY 11/03/2015: GTA Online players struggled to connect to the game following the release of four-player co-op mode Heists yesterday.

It seems Rockstar's servers struggled to cope with the influx of players, a problem that affected all versions of the game.

But Xbox Live users were worse off, with some reporting problems with joining games, downloading content they'd already bought, and even signing in to their profile.

"We are aware of some issues today with players having problems connecting to GTA Online, as well as issues with the Xbox Live service," Rockstar said in a statement published on its support website.

"We are working to restore full access to GTA Online as quickly as possible. In the meantime, please stay tuned to this page to monitor the performance of all platforms."

Currently all versions of the game appear to be up and running, but there is an Xbox Live status alert for downloading items you've already bought, relating to the Xbox 360.

The following message was posted on the Xbox Support website late last night:

"Hey Xbox members, if you are having difficulties trying to download Themes and Gamer pics, we're aware of the issues and are working hard to get them resolved ASAP. Thank you for being patient! We'll post another update as soon as we have more information."

Messages of complaint continue to batter the Rockstar Support Twitter account, which has been working throughout the night and into this morning.

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@RockstarSupport @_AMLHKIM_ I CAN'T GET ONLINE — Jesse Grantham (@grantham_jesse) March 11, 2015

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@RockstarSupport man all day long trried to play heists cant play though cause everything keeps screwing up — Shaun M W (@que_seraaa) March 11, 2015

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We'll monitor the status of GTA Online Heists throughout the day and update this article as necessary.