Pages + Frames = Page Tables
It is the job of the operating system is to keep track of which of virtual-page points to which physical frame. This information is kept in a page-table which, in its simplest form, could simply be a table where each row contains its associated frame — this is termed a linear page-table. If you were to use this simple system, with a 32 bit address-space and 4 KiB pages there would be 1048576 possible pages to keep track of in the page table (232 ÷ 4096); hence the table would be 1048576 entries long to ensure we can always map a virtual page to a physical page.
Page tables can have many different structures and are highly optimised, as the process of finding a page in the page table can be a lengthy process. We will examine page-tables in more depth later.
The page-table for a process is under the exclusive control of the operating system. When a process requests memory, the operating system finds it a free page of physical memory and records the virtual-to-physical translation in the processes page-table. Conversely, when the process gives up memory, the virtual-to-physical record is removed and the underlying frame becomes free for allocation to another process.