How to display Linux kernel and version information

List full distribution name:

[root@myserver/]# cat /etc/redhat-release
Red Hat Enterprise Linux Server release 5.2 (Tikanga)

List kernel version:

[root@myserver/]# cat /proc/version
Linux version 2.6.18-92.el5xen (brewbuilder@ls20-bc2-13.build.redhat.com) (gcc version 4.1.2 20071124 (Red Hat 4.1.2-41)) #1 SMP Tue Apr 29 13:31:30 EDT 2008

List processor type:

[root@myserver/]# uname -p
x86_64

List all:

root@myserver/]# uname -a
Linux myserver.mydomain.com 2.6.18-92.el5xen #1 SMP Tue Apr 29 13:31:30 EDT 2008 x86_64 x86_64 x86_64 GNU/Linux

From RHEL 7, you can use "hostnamectl":

[root@myhost ~]# hostnamectl
   Static hostname: myhost.mydomain.com
         Icon name: computer-vm
           Chassis: vm
        Machine ID: ******
           Boot ID: ******
    Virtualization: vmware
  Operating System: Red Hat Enterprise Linux Server 7.8 (Maipo)
       CPE OS Name: cpe:/o:redhat:enterprise_linux:7.8:GA:server
            Kernel: Linux 3.10.0-1127.19.1.el7.x86_64
      Architecture: x86-64

The contributor slm gives a good explaination on the background for hostnamectl in this article on stackexchange.com