Algorithms like Timsort, Quicksort & Mergesort dominate the "real world" sorting methods. The case for these comparison sorts is quite practical — they've been shown to be the most performant, stable, multipurpose sorting algorithms in a wide variety of environments.
However, it seems like nearly everything that we would sort on a computer are countable / partially ordered. Numbers, characters, strings, even functions are amenable to some meaningful non-comparison sorting method. A candidate here is Radix sort. In general it will behave faster than O(n*log(n)), beating the theoretical comparison sort limit of n * log(n) by a wide margin in many cases with a complexity of O(K*n) -- K being the number of bits that are required to represent a particular item.
What gives?
log n
for n distinct items -- that's not really why radix sort can beat comparison based sorts. (2) Introsort is not the only widely-used sorting algorithm, at least two popular standard libraries use Timsort. – user395760