Commutative algebraic groups occur in several areas of algebraic geometry, e.g. as Jacobians of (possibly singular) curves. Their structure is not so well understood in general, and becomes much simpler when considering commutative algebraic groups up to isogeny. For example, every such group has a unique decomposition into indecomposable summands in this setting. The talk will address the category of commutative algebraic groups up to isogeny and the classification of its indecomposable objects, which can be carried out in certain cases by means of valued graphs.