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Which musical forms are commonly used in the first movements of Classical concertos?

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caricature of Antonio Vivaldi — concerto Caricature of Antonio Vivaldi, pen and ink on paper by Pier Leone Ghezzi, 1723; in the Codex Ottoboni, Vatican Library, Rome. The inscription below the drawing reads, “Il Prete rosso Compositore di Musica che fece L'opera a Capranica del 1723” (“The red priest, composer of music who made the opera at Capranica [College in Rome] of 1723”).

In the Classical era (c. 1750–1830), the first movements of concertos are generally based on an approximation of sonata form.12

While textbooks often describe this as a "double exposition"—where the orchestra plays the exposition first in the tonic key, followed by a more elaborate repetition featuring the soloist—this structure was applied with significant flexibility. The application of sonata form in concertos was typically looser than in symphonies or string quartets, largely due to the extensive passagework required to showcase the soloist's virtuosity.12

This structural freedom often culminates in a terminal cadenza near the end of the first movement, providing an opportunity for the performer to display technical brilliance. Because the concerto is defined by the dialogue between the soloist and the orchestra, the construction of these movements is fundamentally shaped by their interrelationship, often leading to variations in thematic organization and the development of musical material.12