Real mode is supported on all x86s (starting with 8086?). In fact, an x86 processor is initially started in real mode (see first instruction of an x86)
Segmentation
8086: 20-bit address, but only 16-bit registers. In order to make entire address space available, segmentation is used.
Memory diveded into 64 KB (16-bit) chunks («segments»). Start address of segment: segment-selector * 16.
Protected mode
32-bit address bus instead of 20-bit.
Paging
In protected mode, real mode (8086) software can be executed in a protected (and multi tasking) environment, called «virtual-8086 mode».
Segmentation
No fixed 64 KB chunks anymore, instead: size and location of segements described by segment descriptor (which are stored in the GDT - Global Descriptor Table).
System management mode (SMM)
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IA-32e mode
IA-32e mode comes with the 64 bit archtecture. It has two submodes:
Compatiblity mode
64 bit mode
Compatiblity mode
Allows most 16- and 32-bit applications to run unchanged.
Compatiblity mode is similar to 32-bit protected mode.
The OS can switch between compatibility mode and 64 bit mode using a code segment.