Most operating systems use LRU or an approximation to it. The page table often includes a reference bit to help do LRU replacement. Write-through does not make sense because of the very large access penalty. Thus, the page table uses a dirty bit to keep track which pages have been modified and must be written to disk before they are replaced. We do not want to write pages to disk that have not been modified.
Page tables imply that a memory reference requires two memory accesses.
One for the page table and one to get the data. A TLB, which caches previous translations, can be effective in reducing memory references to the page table. This works because of the principle of locality. Replacement may be done in hardware or may be assisted by software. Hardware handling is faster, but software is more flexible.