He is very famous for the incidental music he wrote for Henrik Ibsen's 'Peer Gynt', which includes 'In the Hall of the Mountain King' and 'Morning Mood'.
Between the years 1867 and 1901 he wrote ten collections of Lyriske Stykker(Lyric Pieces) for the piano.
He has used a variety of styles of music throughout his career, such as variations of traditional folk music, which he is commonly associated with, songs based off of the late Romantic style, and free sonata form.
During his two visits to Rome, Grieg met Liszt, who reviewed his first violin concerto, which he enjoyed. He also played Grieg's Piano Concerto by sight, which Grieg liked greatly, but couldn't help but to tell him he had played the first movement too quickly.