When and how did the Benediction of the Blessed Sacrament start in the Catholic Church? In some Christian Churches, there is according to Wikipedia, a devotional ceremony known as Benediction of the Blessed Sacrament.

The question is when and how did this ceremony arise within the Catholic Church and what is the theological basis for it?
The Benediction of the Blessed Sacrament is the result of a confluence of two separate traditions dating back to the thirteenth century. Exposing the Blessed Sacrament for veneration in a monstrance grew out of special value being placed upon the act of looking at the elevation of the Eucharist at mass, probably as a form of protest against the theological views of Peter the Chanter. The second tradition, an evening devotion consisting of the singing of certain hymns, litanies, or canticles before the Blessed Sacrament developed from the many confraternities and guilds that sang canticles in the evening before a statue of "Our Lady". 

Summarized from the Benediction of the Blessed Sacrament entry in the 1917 Catholic Encyclopedia