The music of the dance style has only recently been affected by the modern world. Until movies were invented, the music always the traditional South Indian Carnatic style. The main instruments are the veena, flute, mrdangam, and violin.
After movies became popular, the dance was used again as entertainment and with a fusion style of the time, which was mostly influenced by British music. This is mostly recognized as the Bollywood industry's creation. Recently a new genre specifically called fusion music has been created. It is very popular amongst the younger generation, and is usually danced to as a Thillana , or repetitive beats. This type of dance allows for a lot of creativity and is not restricted too much by expression. It allows audiences to enjoy the traditional dance with an upbeat style.
This is a an excellent video to understand how it is taught and gives a more traditional view.
The modern version with fusion music