‘Simple-minded objects’ are generalisations of simple modules. They satisfy Schur’s lemma and a version of the Jordan-Holder theorem, depending on context. In this talk we will consider simple-minded systems (SMSs), which were introduced by Koenig-Liu as an abstraction of non-projective simple modules in stable module categories, and simple-minded collections (SMCs), a variant of SMSs first studied by Rickard in the context of derived equivalences of symmetric algebras. We will explain aspects of the theory of SMSs and SMCs, including mutation and reduction. In particular, we will see that the mutation of an SMS in a general triangulated category is again an SMS, unifying results of Dugas and Jørgensen, and that mutations of strong SMCs are again strong SMCs, giving a conceptual understanding of a result by Koenig-Yang. This talk is based on joint work with Nathan Broomhead, David Pauksztello, David Ploog and Jon Woolf.