Users who purchase on Amazon typically get the following two "recommendations" at the bottom of product page: (1)"Frequently bought together" and (2) "Customers who bought this item also bought".
Strictly speaking, showing what are frequent bought together does not require complex recommender systems. This is a simple counting of frequent itemsets, a very fundamental technique taught on the first day of data mining class. This technique is also called Frequent Pattern Mining. The key challenge here is getting all of those "bought together" sets quickly from billions of transactions.
However, Amazon does provide more personalized recommendation, similar to what Netflix does. After you log in, there is a"recommended for you" page where Amazon's recommendation engine is in full action.
It seems this same implementation has been in use in Amazon until today. As we can see from the picture to the left. The snapshot was taken in January 2013. The first product (Girl’s 7-16 Jacket) is recommended because the user purchased a somewhat similar item (Girls 2-6x Princess Jacket). Similar thing is true for the second recommended product. In other words, item-item similarity is a major technology used by Amazon's recommendation engine.
The field of recommender systems have seen great advance since 2006's Netflix Prize contest. From 2006 until 2009 when the prize was awarded, many methods have been invented to tackle recommendation problem. Among them, the most widely adopted method today is Matrix Factorization (with SVD as a special implementation). It was shown that this method generated better results than item-item similarity approach. Netflix adopted matrix factorization method after 2007, and has been using it in its production system until today.
Both item-item similarity and matrix factorization approach have been eclipsed by other approaches in the last 2 years. Netflix itself has moved into a machine-learning based ranking model, and others (such as getJar, see an early blog) have explored neighborhood-based methods.
Would Amazon adopt more sophisticated methods to make its recommendation? Given its business is doing so well with simple methods, this probably will not happen soon.