Unterberger was the eldest son of an art dealer based in Innsbruck. After completing normal school, he attended the Academy of Commerce in Munich, but soon switched to the Academy of Fine Arts, where he was taught by Professors Clemens von Zimmermann and Julius Lange. In 1858 he followed his mentor Professor Lange, who at the time was the private tutor of Archduchess Charlotte of Belgium, to Milan. However, the war events of 1859 soon forced him to return to Munich.
After only a short stay in the Bavarian metropolis, he went to Düsseldorf, where the landscape painters Andreas and Oswald Achenbach steered his talent into new directions at the local art academy. At that time, Unterberger took on the middle name Richard. At the suggestion of his teachers, he traveled to Norway in 1860, where numerous works were created. His work has been exhibited in Innsbruck, Vienna and Düsseldorf and has been consistently rated favorably by art critics. Spurred on by this success, the artist also toured Denmark and the English and Scottish coasts.
Even in his closer home, Unterberger repeatedly found motifs that inspired him. On the occasion of a stay in Tyrol in 1862, the game was created near Innsbruck with the sunny, illuminated Waldrastspitze in the background, which Archduke Karl Ludwig bought.
In 1864 Unterberger left the Academy in Düsseldorf and moved to Brussels as a freelance painter, which he chose for his permanent residence. From there he visited southern France and - towards the end of the 1960s - also southern Italy. The first Italian picture, a lot near Naples, was exhibited in the Wiener Kunstverein in 1868. At the world exhibition in Vienna in 1873 he presented the picture Sorrento, Gulf of Naples. The sunny coastal landscapes of the Adriatic, but also Venice with its magnificent buildings, picturesque corners and the goings-on of the people soon became the focus of his artistic work for Unterberger. Like hardly any other artist, he knew how to liven up his pictures figuratively without distracting from the main motif.
Unterberger showed particular interest in the Tyrolean State Museum, which owns several of his works, including the painting Amalfi and the Gulf of Salerno.
While a game was on public display on the island of Capri in 1870, Unterberger created two pictures of Lake Achensee. At the Tyrolean national exhibition in 1893 he was represented with the paintings Motif from Denmark, Posilippo Gulf of Naples and Amalfi, Gulf of Salerno. In later times he no longer chose Tyrolean landscapes for his depictions; only a small picture from the Dolomites, Cimone della Pala is known as such.
Unterberger was lucky enough that his pictures were mostly sold away from the exhibitions. At the international exhibitions in Munich, his pictures were usually on display in the Belgian section. Even more often than in Munich he was represented at exhibitions in Brussels, Paris and London, where he was far more known and his name was more popular than in Austria. He has also been awarded medals several times. In 1874 he was awarded the Knight's Cross of the Franz Joseph Order by Emperor Franz Joseph I.
His appearance was elegant and his manners impeccable, with the experiences and insights gained on his travels undoubtedly being of great benefit to him. Despite or because of this sophistication, he remained a bachelor. When he wasn't traveling, he lived in Brussels. From May to July he stayed regularly in Neuilly, a suburb of Paris, where he also had a studio. He died on May 25, 1902 of complications from a stroke. His body was transferred to Innsbruck and buried in the family crypt.
In 1987 the Tyrolean State Museum Ferdinandeum commemorated the life and work of this important Tyrolean artist with a retrospective for the 150th birthday.