How does radix sort work and what is its complexity?

Radix sort sorts integers digit by digit from least significant to most significant (LSD) or vice versa (MSD). Each digit pass uses stable counting sort. For n numbers with d digits and base b (typically 10 or 256), time is O(d*(n+b)), space is O(n+b). When d is constant, achieves O(n) - faster than comparison sorts' O(n log n) lower bound. Best for fixed-length integers or strings.