[1] Groven has contributed to over 250 recordings, and has written more than 350 original compositions, from children's songs and instrumental ballads to movie and TV soundtracks, and works on a larger scale.

He has written music to lyrics and poems by Ove Røsbak, Halvor J. Sandsdalen, Tarjei Vesaas, Olav Kaste, Hans Børli, Josef G.Larssen and Erik Bye.

Composers who have written music especially for Groven include Hui Cheung Wai, Øistein Sommerfeldt, Terje Rypdal, James Moody, Johan Kvandal, Oddvar S. Kvam, Ketil Bjørnstad, Kristian Lindeman, Henning Sommerro, Iver Kleive, Egil Kapstad, Kenneth Sivertsen, Johan Øian, John Surman, Siegfried Steinkogler, Lars Tilling, and Fried Walter.

Reodors ballade (by Bent Fabricius-Bjerre) from the movie "Flåklypa Grand Prix", "Svalbard theme" by Bøhren & Åserud, and a version of Henning Sommero's "Vårsøg" are among the instrumental classics of Norwegian music, loved by several generations.

He has been featured at festivals and major events in Washington (Smithsonian Institution), Los Angeles, San Francisco, Minneapolis, Dallas, Houston, New Orleans, Toronto, most major cities in western Europe as well as Budapest, Belgrade, Athens, also Riydah, Jeddah, Hong Kong, Taipei, Seoul, Kyoto, Singapore and Yokohama.

1975: Så spiller vi harmonica 1976: Music for two Harmonicas (with Tommy Reilly) 1977: Musikk for en lang natt (with Ketil Bjørnstad) 1979: Motlys 1981: Musikken inni oss (with Arve Tellefsen) 1981: Kom sol på alle mine berg (with Geirr Lystrup) 1981: Lævandes dikt (with Ove Røsbak, Iver Kleive) 1983: Songar utan ord (with Henning Sommerro) 1986: Colour Slides 1988: Aria 1988: Sigmund Groven (compilation) 1990: Nordisk natt 1991: Nattønsker (compilation) 1993: Siesta 1995: Til Telemark 1996: I godt lag (compilation) 1998: Harmonica Album 2000: Innunder jul (with Iver Kleive, Anne Vada) 2001: Vi på Langedrag (TV documentary soundtrack) 2003: Over the Rainbow 2004: Here, There and Everywhere (with The Norwegian Radio Orchestra under the direction of John Wilson) 2005: PhilHarmonica (with The Norwegian Radio Orchestra under the direction of Christian Eggen) 2007: Grieg Album (with Ivar Anton Waagaard, Kåre Nordstoga, and The Norwegian Radio Orchestra under the direction of Peter Szilvay) 2010: HarmOrgan (with Iver Kleive) 2012: Classical Harmonica 2014: Sigmund Groven Collection vol.