Jazz and blues continue to profoundly influence American popular music.
Jazz and blues both developed around the turn of the 20th century, mostly within African-American communities throughout the southern United States. The two styles have declined in popularity since the middle of the 20th century, and much of their cultural energy has been absorbed by other styles. But both jazz and blues live on today and are therefore "modern music" themselves, and you'll hear their influence in other genres as well.
Rock and Roll
Rock and roll emerged in the 1950s as an outgrowth of the blues. For a while, the two genres could be difficult to separate. Early rock and roll often used the same chord progressions as the blues and had a similar "one-TWO-three-FOUR" rhythmic approach. Rock and roll eventually emerged as a genre with louder drumming, lyrics designed to appeal to young audiences, and, sometimes, a pronounced country music influence. Rock music today often (although not always) uses chord progressions that are distinct from the blues but usually retains its basic rhythmic feel.
Hip Hop
Hip hop lyrics and blues lyrics are both often matter-of-fact, and they often embrace dark themes and difficult situations. Fro example, there is a connection between the narrative-based lyrics of jump blues artist Louis Jordan's 1949 hit "Saturday Night Fish Fry" (which details a Saturday-night party that gets shut down by the police) and contemporary hip hop lyrics. Also, freestyle rap, in which the performer improvises lyrics, parallels improvised instrumental solos in both jazz and the blues.
R&B
Rhythm and blues (R&B) is an umbrella term that refers to styles as diverse as soul, disco and funk. The rise of disco in the 1970s and the hip-hop-influenced New Jack Swing style in the 1980s changed R&B backing tracks so fundamentally that they no longer resemble the blues. But the emotive vocal style of contemporary R&B singing is derived partially from the blues (as well as from gospel music). Modern R&B singers such as Beyonc Knowles and Alicia Keys use bends and melismas (more than one note per syllable) much like those of blues singers such as Etta James.
Studio Musicians and Backing Bands
Many professional musicians who accompany famous pop singers, either in performance or in the studio, are jazz musicians. For example, guitarist Tariqh Akoni has performed with Christina Aguilera and the Backstreet Boys, but Tariqh is also trained in jazz. Jazz players often perform well in such situations due to their abilities to sight-read, respond to musical stimuli, and adjust to different performance contexts. The complex harmonies and nimble rhythms of jazz are the training ground for musicians who wish to play other forms of popular music, particularly in situations where there might not be an ideal amount of time for rehearsal.