How does quick sort work and what is its average complexity?

Quick sort selects a pivot element, partitions the array so elements less than pivot are on the left and greater on the right, then recursively sorts the partitions. Average time complexity is O(n log n), worst case O(n^2) when pivot is always smallest/largest. Space is O(log n) for recursion stack. Fast in practice due to cache efficiency and in-place sorting. Pivot selection strategies (random, median-of-three) help avoid worst case.