Alvi Joensen was born and raised in a little town on Faroe Islands called Norðagøta. His fascination with music started with father playing the piano and the accordion. He started out playing piano, but soon his interest turned to the electric guitar and rock music. When Alvi was eleven years old he played his first classical guitar piece, from then on he was hooked.

Few years later he went to a music highschool in the capital of Faroe Islands with classical guitar as his main subject. Nineteen years old he continued his studies of classical guitar in the Music Academy of Malmoe under the guidance of Gunnar Spjuth and Prof. Göran Söllscher. In 2017 Alvi Joensen finished his Diploma-studies, the highest academic degree in music performance.

Alvi Joensen has participated in a few competitions, one of which he has won a 1st and 2nd prize. He has attended many festivals and regularly plays in one for contemporary music in Faroe Islands. Alvi has also appeared as a soloist with orchestra. Twice with the Faroese National Symphony Orchestra playing Rodrigo's "Fantasia para un Gentilhombre" and "Concierto de Aranjuez". For the final examination concert of his Diploma-studies he commissioned  a new guitar-concerto from the renowned swedish composer Staffan Storm. The premiere performance was made with the swedish string orchestra Musica Vitae, the famous percussionist Johan Bridger and the conductor Jon Gjesme.

Alvi Joensen is also an avid chamber musician and plays regularly in different ensembles. One of his favorit ensembles is the duo with his fellow guitarist and good friend Max Näpel, which is called Nordic Guitar Duo. They received a special mention in the Young Talent Competition on Uppsala Guitar Festival 2015 with the motivation: "An energetic and colorful performance"