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.
The father of modern classical guitar, Andres Segovia (Spain), performing Isaac Albeniz's great piece "Asturias (Leyenda)." Segovia brought the guitar up to the level of art, at least in the minds of classical musicians, and made all that came after him possible. Information on Andre Segovia can be found here.
I've heard it said that Julian Bream has a perfect right hand on the guitar. He is often described as the most musical guitarist. More info here.
"Recuerdos de la Alhambra" is one of the most famous guitar pieces ever writen. The name means "memories of Alhambra," which is a palace/fortress in Spain. The piece utilizes one of the rare techniques that are unique to the guitar, tremolo.