Modern (Serious) is the term used to describe "serious" music written roughly after the start of the 20th century. The term is contrasted with Popular Modern, which overlaps the same period. My use of the word Serious does not imply that the music cannot be amusing, light-hearted or enjoyable.
A few composers who lived in the first decades of the twentieth century, built on the romantic style of the previous musical period. Examples are Sibelius and Holst.
However, the period is dominated by composers who try to do something different. For them, it was, and continues to be, a kind of musical revolt. Everything many of them wrote was driven by an urgent desire to be completely new, utterly different, with little or no connection to the masterpieces of earlier centuries.
They abandoned the conventions of harmony and cadences, so a listener would be deliberately left hanging on a dominant or diminished chord.. They abandoned the distinction between consonance and dissonance. In earlier music, dissonance was used rarely, and usually only in passing on to a consonance. In modern music, dissonance is almost more common than consonance, and it still sounds jarring to many ears today.
They abandoned conventional tonality, in which the music starts and ends in a recognizable key, and is centred on one tone and its tonic chord. Instead they introduced the 12-tone scale, which uses all 12 of the chromatic tones in the equi-tempered octave, and has no feeling of a 'home' note or resting place.
The use of percussion has increased enormously in this period. All sorts of exotic percussion instruments are utilized in musical works, from African drums to vacuum cleaners, from Indonesian gamelan gongs to typewriters. Noise has become a valid element in modern (serious) music.
In 1913, at the premiere of a new ballet by Stravinsky, called 'The Rite of Spring', the audience rioted at the cruel dissonance and barbarity of this new music, and the police had to be called in. Since then, audiences have become more broad-minded, though also probably a lot more polite and tolerant of those who want to listen. And people have realized that a lot of Stravinsky's music is worth listening to. So as time goes by, much modern (serious) music will be forgotten, though a few gems will no doubt emerge, as has happened in the past.