[1] Epstein was a pupil at Agram of the choir-director Vatroslav Lichtenegger, and in Vienna of Johann Rufinatscha (composition) and Anton Halm (pianoforte).

From 1867 to 1901, Epstein was a professor of piano at the Vienna Conservatory, where Ignaz Brüll, Marcella Sembrich, Mathilde Kralik, Gustav Mahler, Benito Bersa and Richard Robert were among his pupils.

Epstein edited Beethoven's piano sonatas, Mendelssohn's "Sämmtliche Klavierwerke" and Schubert's "Kritisch Durchgesehene Gesammtausgabe", among others.

Epstein was a good friend of Johannes Brahms, Ferdo Livadić and mentor of Gustav Mahler.

[1][2] In 1902, Epstein received the Knight's Cross of the Order of Franz Joseph to commemorate his seventieth birthday.