These compositors belong to the 20th century "Second Viennese School", they are characterized because they didn't follow up traditional tonality.
Schoenberg was the first to change the traditional way of making music by inventing the twelve-tone system of composition which became known as Serialism. This method uses a series of pitches in certain order, which may then be taken in retrograd form, in inversion and in retrograde inversion, and also in transposition. Berg, and Webern were his pupils, they developed innovative ideas as well.
It is said that this kind of compositions are hard to listen for the common audience.