Popular Modern is the term used for popular songs, ballads, jazz, and rock music, written from the middle of the 20th century onwards. Its most salient characteristic is its enormous popularity. Audiences often fill football stadiums, and record sales frequently pass the million mark.
Another characteristic is the relative importance of the performers, compared to the composer. Often the artists performing a song have written it themselves. If not, it is their performance of the song that gives it its character, and the name of the actual composer is probably unknown to everyone involved. Fans follow performers, not composers. Record and CD labels display the names of performers, not composers.
Popular songs and ballads have much in common with folk music. This applies especially to songs popular between 1910 and 1960. They usually are short, have simple memorable tunes, and easily memorable words. Bing Crosby and Frank Sinatra sang these kinds of catchy tunes, and they were idolized by fans in their heyday. In this period, the musical was a development from light opera, in which songs were strung together with a story. My fair Lady and Oklahoma are fine examples of this genre, and the tunes from these musicals are still heard frequently to the present day.
In the USA, jazz evolved from black spiritual songs, mixed with blues, marching band music and ragtime piano music. In its evolution, jazz passed through Dixieland/New Orleans/Traditional Jazz style, to Swing, to Big Band, then to Modern Jazz, and finally more or less faded out in 1960 with its evolution into 'Free jazz', in which every player played what they felt like.
Rock music started in the 1960s as rock'n'roll, as an evolution from rhythm and blues combined with country and western. It was characterized by a heavy beat on drums and cymbals, simple chord progressions, and a catchy melody. Since then it has evolved into many variations of rock, including punk, progressive, and heavy metal. It is way beyond the scope of Best Classical Tunes to demonstrate, describe or analyse these types of music.