Microsoft has announced that the .NET Core 2.0 will be considered "end of life" and thus no longer supported as of October 1, 2018. .NET Core 2.0 is considered a non-LTS release, and as such Microsoft only commits its support for three months after a successor has been released. In this case, with .NET Core 2.1 having been released May 31, .NET Core 2.0's end has come.
Astute readers will note that October is more than three months from May 31. The reason for this increased lifespan is due to a critical bug that is affecting some users who are attempting to upgrade from .NET Core 2.0 to .NET Core 2.1. The issue is an application crashing exception ("System.BadImageFormatException") that can occur when the "AppDynamics.Agent.Windows" package is part of a web application. Microsoft has reproduced the issue and agrees that it is a blocking item. As such a fix for this bug will be released in the .NET Core August 2018 update. Microsoft's goal is for the users affected by the bug to then have approximately six weeks to then upgrade to .NET Core 2.1.
Microsoft .NET Core developer Noah Falk has provided additional details on the matter, observing that fixing this bug increased the severity of an additional known issue that will also be fixed. Preview builds will be available shortly for those looking to confirm the fix on their systems prior to the release of the official update.
As Microsoft's Rich Lander notes, .NET Core 2.1 will be a long-term support release (LTS) so developers on older platforms should plan to upgrade to it as soon as possible. Upgrade instructions for migrations to .NET Core 2.1 and ASP.NET Core 2.1 are available now and it makes sense to start making preparations now.
If you're interested in digging deeper into Microsoft's support policy for .NET Core, they have prepared a detail document explaining the differences between a regular release and one considered LTS. Related to this is a full list of operating systems supported by .NET Core.