Jazz piano has been a part of jazz since its beginnings. Piano is one of the rare instruments in a jazz combo which can play chords, unlike saxophone or trumpet which can only play single notes. The early jazz piano was mainly stride. Stride is also known as New York ragtime is a pioneering jazz piano style. It was developed in Harlem during the World war one. As you can see from the name (New York ragtime) it was influenced by ragtime but it featured improvisations, blue notes and swing rhythms which were new in this type of music.
The great performers of that time were Earl Hines, James P. Johnson, Jelly Roll Morton, Willie "The Lion" Smith , Art Tatum, Thomas "Fats" Waller, Mary Lou Williams, Teddy Wilson and many others who often attended cutting contests (battles between stride piano players in the early 1920s) where they showed of their skills.
It continued to develop specially during the 50s and 60s with pianists like Red Garland and McCoy Tyner. In that time one of the most widely spread types of jazz called Free Jazz was becoming more and more popular. Some great works of art still reminds us of that time which surely was a gold age of jazz existence. The beginnings of free jazz can be set with recordings of Ornette Coleman for Contemporary and with the Jazz Advance and Looking Ahead, two great albums by Cecil Taylor.
Today jazz piano is still popular among many pianists just to mention few Michael Weiss, Bill Charlap, Geoffrey Keezer, Brad Mehldau, Mulgrew Miller, Danilo Perez and many others.