In the case of external sorting (on hard drive(s)), a copy of a post I made in another thread:
As far as I know, most external sorts use k-way merge sorts (with k = 8 or more) combined with large I/O's (large number of elements read or written per read or write) to reduce the overhead of random access on hard drives with higher k-way merge sorts.
I doubt any one uses tape drives for sorting anymore, but an alternative to merge sort was poly phase sort, a variation of merge sort that deliberately distributes data unevenly in a special pattern on the tape drives. Poly phase sorts could have been used on hard drives back when memory was limited, but on modern computers, there's enough memory to use large I/O's, reducing the overhead of increased random access in a higher k-way merge sort, and higher k-way merge sorts are faster than poly phase merge sorts (when k is 6 or greater, sometimes when k is 5).
On some mainframes, the I/O controllers can be programmed to write elements via pointers to the elements in a single I/O, speeding up a sort (via a modified device driver or special I/O call to the device driver). These type of controllers are called vectored I/O or scatter / gather. PC's have these type of controllers for hard drives, but scatter / gather is used for the scattered 4k blocks of physical memory that make up what appears to be a continuous virtual memory address space.
External sorting - Wikipedia, the free encyclopedia
Polyphase merge sort - Wikipedia, the free encyclopedia
Vectored I/O - Wikipedia, the free encyclopedia