unfortunately this page got deleted by accident, this version is restored from https://web.archive.org/web/20150318062024/http://kernelnewbies.org/y2038, but most of the formatting is still missing.
The year 2038 problem
All 32-bit kernels to date use a signed 32-bit time_t type, which can only represent time until January 2038. Since embedded systems running 32-bit Linux are going to survive beyond that date, we have to change all current uses, in a backwards compatible way.
User space interfaces
We will likely keep the 32-bit time_t in all user space interfaces that currently use it, but add new interfaces with a 64-bit timespec or another type that can represent later times. Most importantly that impacts system calls, but also specific ioctl commands and a few other interfaces. User space programs have to be recompiled to use the new interfaces, and the policy whether to use the old or the time time is left to the C library. While that policy is a complex topic itself, we don't cover it here.
System calls
System calls have been moved out [y2038/syscalls], that page is rather outdated, newer information is available at https://lwn.net/Articles/643234/
File systems
Each file system stores its file modification times in its own format on disk, and a lot of them have the same problem. See also [y2038/vfs].