John Williams (Australia), guitarist, and Joaquin Rodrigo (Spain), composer.
John Williams is one of the greatest living guitarists. He has performed virtually all of the classical guitar repertoire and even had a rock band. His Wikipedia page can fill in some details on him.
This concerto is THE guitar concerto to which all others are compared. Concertos typically consist of three movements (separate pieces that are played together and often share some musical elements). This concerto is very Spanish, since the composer Joaquin Rodrigo is from Spain, and is comprised of a fast, slow, and another fast movement.