This thesis analyses the problem of sorting on modern architecture presenting the most recent results in the literature.

It also provides a systematic analysis of the solutions available in a real world scenario: a DBMS where the performance of the sorting algorithm is a critical aspect being a basic brick to serve even the most trivial requests like merge operations.

Moreover it analyses the learned sort algorithm in depth and describes different alternatives for the learned index to be used in this context, proposing an innovative alternative to the current one.