Pick a pivot, partition, recurse. Fast in practice.
Pick a pivot, partition the array so smaller values sit left and larger right, then recurse on each side. The partition does the heavy lifting; the recursion is often implemented with one real call and one tail call to keep the stack small.
General-purpose in-memory sorting of large arrays. Excellent cache behavior and tiny constants make it the fastest option in practice on random data — C's qsort and the unstable sort in many language runtimes are quicksort variants.
Adversarial or already-sorted input with a naive pivot choice collapses to O(n²). It also isn't stable — reach for mergesort or TimSort when equal-key order must be preserved.