Masterpieces in which timpani are used for solos
It was probably around the 20th century, around the time that the pedal timpani was devised, that the instrument began to gain recognition as a solo instrument. Of course, there was music composed in the 18th century that featured eight timpani to create a scale for a timpani solo. However, it wasn't until the 20th century that the possibilities for the timpani as a solo instrument became widely pursued.
Here's an example of a relatively well-known piece by Poulenc, a French composer during the first half of the 20th century.
F. Poulenc: Concerto for Organ, Timpani and Strings in G minor
As a piece that featured the timpani as a solo instrument, this is likely one of the most famous concertos by Poulenc. This work was commissioned by Princess Edmond de Polignac and composed in 1938. Although the tone of this piece is grounded in its resounding Bach-style organ, and Poulenc himself thought of this piece as a religious work, the sounds of timpani both join and contrast with the organ and string ensemble, giving the timpani a rather important role in its performance.