Some remarks on the affineness of A^1-bundles

We study how forcing algebras give rise to ${\mathbb{A}}^1$-bundles and ${\mathbb{A}}^1$-torsors and how they are related to ${\mathbb{A}}^1$-patches. In particular we discuss the affineness of torsors and how algebraic properties of ${\mathbb{A}}^1$-patches can be deduced from this property. This is in part a survey article.