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Classical and romantic 
As the piano developed and became accepted, composers naturally started writing concerti for it. This happened in the late 18th century, during the Classical music era. Wolfgang Amadeus Mozart was the most important composer in the early development of the form. Mozart's body of masterly piano concerti put his stamp firmly on the genre well into the Romantic era.
Mozart wrote many piano concertos for himself to perform (his 27 piano concertos also include concerti for two and three pianos). With the rise of the piano virtuoso, many composer-pianists did likewise, notably Ludwig van Beethoven, Frédéric Chopin, and Robert Schumann—and also lesser-known musicians like Johann Nepomuk Hummel, Joseph Wölfl, Carl Maria von Weber, John Field, Ferdinand Ries, and F. X. Mozart.
Well known examples from the middle to late Romantic era include concerti by Edvard Grieg, Johannes Brahms, Camille Saint-Saëns, Franz Liszt, Pyotr Ilyich Tchaikovsky, and Sergei Rachmaninoff. Antonín Dvořák and Franz Xaver Scharwenka wrote some lesser-known concerti during this time. Edward Elgar made sketches for a piano concerto but never completed it.
In the 19th century, Henry Litolff blurred the boundary between piano concerto and symphony in his five works entitled Concerto Symphonique, and Ferruccio Busoni added a male choir in the last movement of his hour-long concerto. Wilhelm Furtwängler wrote his Symphonic Concerto for Piano and Orchestra, which lasts more than one hour, in 1924-1937. In a more general sense, the term "piano concerto" could extend to the numerous often programmatic concerted works for piano and orchestra from the era – Beethoven's Choral Fantasy, Liszt's Totentanz and Ruins of Athens Variations, and Richard Strauss's Burleske are only a few of the hundreds of such works.
The few well-known piano concerti that dominate today's concert programs and discographies comprise only a small part of the repertoire that proliferated on the European music scene during the 19th century.
20th century and contemporary 
The piano concerto form survived through the 20th century into the 21st, with examples being written by Arnold Schoenberg, Béla Bartók, Igor Stravinsky, Sergei Prokofiev, Nikolai Medtner, Alexander Tcherepnin, Maurice Ravel, George Gershwin, Michael Tippett, Charles Wuorinen, York Bowen, Frank Martin, Bohuslav Martinů, Peter Mieg, Heinrich Sutermeister, Dmitri Shostakovich, Samuel Barber, Witold Lutosławski, Gian Francesco Malipiero, Peter Mennin, György Ligeti, Elliott Carter, Selim Palmgren, Leroy Anderson, Emma Lou Diemer, and others.
Parts of other 20th century symphonic works give the piano occasional prominence like any other instrument of the orchestra, as in the Symphony in Three Movements by Igor Stravinsky, Samuel Barber's violin concerto, and the Symphony No.3 by Michael Tippett.
Works for piano left-hand and orchestra 
The German Paul Wittgenstein lost his right arm during World War I, and on resuming his musical career asked a number of composers to write pieces for him that required the left hand only. The Czech Otakar Hollmann, whose right arm was injured in the war, did likewise but to a lesser degree. The results of these commissions include concertante pieces for orchestra and piano left hand by Bortkiewicz, Britten, Hindemith, Janáček, Korngold, Martinů, Prokofiev, Ravel, Franz Schmidt, Richard Strauss, and others.
Works for two and more pianos and orchestra 
Concertos and concert works for two pianos were written by Bach (two to four pianos, BWV 1060-65, actually harpsichord concertos, but often performed on pianos), Mozart (two, K 242 (originally for three pianos and orchestra) and K 365), Mendelssohn (two, 1823-4), Bruch (1912), Béla Bartók (1927/1932, a reworking of his Sonata for two pianos and percussion), Poulenc (1932), Arthur Benjamin (1938), Peter Mieg (1939-41), Darius Milhaud (1941 and 1951), Bohuslav Martinů (1943), Ralph Vaughan Williams (c. 1946), Roy Harris (1946), Gian Francesco Malipiero (two works, both 1957), Walter Piston (1959), Luciano Berio (1973), and Harald Genzmer (1990). Apart from the Bach and Mozart examples, works for more than two pianos and orchestra are considerably rarer, but have been written by Carl Czerny (Quatuor Concerto for four pianos and orchestra, op. 230), Morton Gould (Inventions for four pianos and orchestra, 1954), Peter Racine Fricker (Concertante for three pianos, timpani, and strings, 1956), and Wolfgang Fortner (Triplum for three pianos and orchestra, 1966)
A classical piano concerto is often in three movements.
- A quick opening movement in sonata form including a cadenza (which may be improvised by the soloist).
- A slow, free expressive movement
- A faster rondo
Examples by Mozart and Beethoven follow this model, but many others do not. Beethoven's fourth concerto includes a last-movement cadenza, and many composers introduced innovations. Liszt's concerti are played without a break, though separate movements are clearly evident.
One example of a concerto in only one discrete movement (Allegro brillante) is Tchaikovsky's Piano Concerto No. 3 in E-flat major (1893).
See also 
- List of compositions for piano and orchestra
- List of piano concertos by key
- List of works for piano left-hand and orchestra
- Concerto for solo piano
- Maurice Hinson, Music for Piano and Orchestra, an annotated guide, Indiana University Press, 1993
- Hyperion's Romantic Piano Concerto Series (a commercial website selling recordings on CD)
- Rachmaninoff's Works for Piano and Orchestra An analysis of Rachmaninoff's Works for Piano and Orchestra including the Piano Concertos and the Paganini Rhapsody.
- Classical and Romantic Piano Concertos, an extensive list of Classical and Romantic piano concertos, and other music for piano and orchestra from the same period.
- Music for Piano and Orchestra: The Recorded Repertory, An exhaustive list of recorded works for piano and orchestra.