The history of modern sheet music, at least in the West, can be appropriately begun with the advent of the printing press in the middle of the 15th century. Until this time, music had been handwritten and generally preserved in large, bound volumes of manuscripts. The shift from handwritten to machine-printed did not occur overnight, and much music continued to exist solely in manuscripts until well into the 18th century. However, no one will argue that just as the printing press changed the history of the written word, so it also altered the course of sheet music.
The first printed book to include music was the Mainz psalter, a collection of psalms, and it was printed in 1457 by Johann Fust and Peter Shoffer. However, these gentlemen had not yet managed to figure out how to print music using movable type, the result being that the musical notation was added in by hand. It was not until 1473 that the first machine-printed book was produced, and it was still a long and laborious process and the result was less than perfect. Improvements continued to be made, however, and in 1501 the Harmonice Musices Odhecaton A, which contained 96 pieces of clean, readable music, was printed. It required three passes through the printing press, but it was still a step forward. This process was later reduced to two passes and finally, in 1520, to a single pass.
The printing press, as mentioned, had an unprecedented effect on the written word, and its affect upon written music was similar. Beginning in the early 16th century, sheet music could be spread faster, more efficiently, and to more people than ever before. Professionals had a much wider array of music at their disposal. Amateur musicians suddenly had better access to affordable music. This had the affect of creating a much wider pool of amateur musicians, who the professionals could then teach and thereby earn a livelihood. The entire music industry of the Renaissance Period was affected, and the industry of printed sheet music was permanently established.
Of course, in the early years of printed sheet music, its distribution was certainly limited by its cost. And in many places, the right to print music was granted by the monarch, which meant that a printer had to gain special dispensation in order to produce sheet music. Nevertheless, the industry of printing sheet music snowballed over the next few centuries and by the 1800s, it was everywhere, the dominant force in the music industry.
In the United States, sheet music gained importance due to the unfortunate pervasiveness of "blackface" theatre. Around the same time, parlor music exploded in popularity and every middle class home needed a piano and the sheet music that went with it. It was not until the advent of the phonograph in the early 20th century that that sheet music began to lessen in importance. The invention of the radio in the 1920s furthered the trend and eventually, the record industry replaced sheet music publishers as the music industry's most influential force.