She was awarded the Nordic Council Literature Prize in 1998 for the poetry collection Efter att ha tillbringat en natt bland hästar.

In the collection After Spending a Night Among Horses (Efter att ha tillbringat en natt bland hästar) (1997) Forsström uses quotations from the Andrei Tarkovsky film Stalker, they are placed as interludes in a sequence of pieces and sit alone on the page, without direct reference to their source on the page, leaving this to a Notes & Quotations section at the end of the book.

Her breakthrough into the English-speaking world came in 1987 with her sixth collection, Snow Leopard (Snöleopard), which was translated into the English by David McDuff and published by Bloodaxe Books.

In 2006, I Studied Once at a Wonderful Faculty was published by Bloodaxe Books, with translations from David McDuff and Stina Katchadourian.

The collection contains Snow Leopard (Snöleopard) (1987), The Parks (Parkerna) (1992), After Spending a Night Among Horses (Efter att ha tillbringat en natt bland hästar) (1997) and a new poem sequence called Minerals.