For an artin algebra $\Lambda$, cotorsion pairs are studied for the category ${\rm mod}\Lambda$ of finitely presented $\Lambda$-modules and for the category ${\rm Mod}\Lambda$ of all $\Lambda$-modules. It is shown that every cotorsion pair for ${\rm mod}\Lambda$ induces a cotorsion pair for ${\rm Mod}\Lambda$. This has some interesting applications, even for the category of finitely presented modules. Another theme of the paper is the interplay between cotorsion and torsion pairs. This leads to a conjecture which is an analogue of the telescope conjecture in stable homotopy theory.