A viola concerto is a musical composition featuring a solo viola and supporting orchestra. Similar to concerti for other instruments, a viola concerto usually has multiple movements. The purpose of a viola solo is to highlight the level of expression and technical ability a viola player has, but because the word "concerto" means to play off of each other in an almost fighting or dueling style, the supporting orchestra also must be of substantial ability.
Viola concerti are somewhat of a rarity, meaning that although examples certainly do exist, they are present in far fewer numbers than concerti for other instruments. This has to do with how the viola developed. It also has to do with the role the viola usually plays in ensembles and its acoustical properties.
Prior to the 16th century, stringed instruments played with bows were present, but they were different than the members of the modern violin family in overall design, size and number of strings. Scholars are not certain which member of the modern violin family developed first, but some experts believe that, based on linguistic evidence and the presence of certain terminology in musical documents and scores, the viola developed first. Even so, this did not happen until the mid to late 1500s. Instrumental concerti for any instrument did not begin to appear until the end of the 1600s because the instruments available did not allow as much virtuosity, and because it took time for musicians to move past preconceived ideas about how and what to compose.
The fact it took time for the entire violin family to develop and become refined meant that it was not until the baroque period, or roughly 1650 to 1750, that composers first looked at the viola as a solo instrument. An example of a viola concerto written during this period is the Viola Concerto in G Major by Georg Philip Telemann. Some musicians believe this is one of the earliest viola concerti composed, if not the first. A handful of composers tried their hand at writing concertos for the viola, as well, but similar to other forms, the viola concerto fell out of favor until the 20th century when composers "discovered" the viola again.
Composers never really latched onto viola concerti because, although having a tone that is quite beautiful in its own right, the viola functionally usually is a supportive instrument. It plays harmonizing pitches or countermelodies, serving as an inner voice in ensembles. Due to the viola's pitch range, the viola suffers the same problem as the cello in that it is very difficult for players to project their sound easily over that of the accompanying orchestra. This is less of a problem with a chamber orchestra of 50 players or fewer, but standard orchestras may have as many as 100 players. Another issue is that the violin is a more popular instrument, which makes it difficult for composers to choose the viola when they want to ensure the composition will become notable or get programmed on concerts.
On the technical side, viola concerti usually are in the "Italian" concerto form. This means there are three movements, with the first fast, the second slow and the last fast. This form became popular after the Baroque period, during which the concerto usually had four movements of slow, fast, slow and fast tempos. Classical viola concertos of three movements usually follow sonata form for the first movement, ternary form for the second movement and rondo form for the last movement.