Here is a good explain about Tim sort, and I found this 'sound of sorts' quite amazing:
Although in the worst case, the time would be O(nlogn), just like the other sorts, but because this sort can take advantage of the sorted part of the original list, in real world near-sorted cases it can be much better.
But compare to Quicksort, it occupies more memory space(O(logn) to O(n))and may be slower on average. What's more, Quicksort is really simple to write and understand, while Timsort, which is a hybrid sorting algorithm, is not that easy and clear.