It is very hard for a new piece to suddenly become "the new classic" especially after piece like Romance and Recuerdos have been around forever. 
Cavatina was part of the music track of a TV series and composer Stanley Myers developed it into a full piece under the insistence of Australian guitarist John Williams. It later became the soundtrack of award winning movie the "deer hunter", a Vietnam saga with a  great cast of actors including Robert de Niro, Maryl Streep and Christopher Walken. John Williams later performed it in  duo (with orchestral accompaniment) with singer Cleo Lane.

Just like with every great thing in life, simplicity is at the base. Melodically and harmonically Cavatina is simply straightforward and it reaches climaxes in a gentle though powerful way. Technically, Cavatina is very challenging. The solo guitar tries to reproduce the guitar duo performed by Williams in the movie soundtrack version. Keeping the melody separated and at the same time very much bonded and dealing with the long succession of barres throughout different sections of the piece, calls for a not less than perfect fingering and the correct use of the playing apparatus. 

Cavatina's main technical challenge is the long succession of barres which, besides presenting difficulties of their own, pose the extra bonus of having to produce a smooth sounding melody. Achieving all this while intense force is applied to the left hand is a conquest. 

This is one of the few guitar pieces I wanted to play from the first moment I heard it. 

Play the melody using fijación* in finger 4.
 

Click here for TAB

Using the concept of fijacion*, you can play consecutive notes from the main knuckle using the same right hand finger. What you have played to this point is probably as tough as it gets with Cavatina. Everything is pretty much downhill from here. 

Part 1 ends here and the whole section is repeated with only a minor change in the final cadence.

The animation shows how the whole body gets involved to spread the fingers and reach the high D. The fingers are not left alone but they work in conjunction with the arm and the rest of the body.

This is a progression that leads to a beautiful halt just a few measures ahead. Avoid squeaks at all costs using the arm.