Today’s technology is not possible without optoelectronic devices such as light-emitting diodes, transistors and solar cells. These basic units of modern electronic appliancesmay be made not only from traditional inorganic semiconductors, but also from organic semiconductors, i.e. hydrocarbonmolecules that combine semiconducting properties with some mechanical properties such as easy processability and flexibility. The weak van der Waals forces that bind the molecules to a solid imply a low dielectric constant, so that coulomb and exchange interactions between electrons are significant. As a result, photoexcitation or electrical excitation results in strongly bound electron–hole pairs, so-called excitons. Depending on the relative orientation of the electron and hole spin, the exciton may be of a overall singlet or triplet spin state. While the fluorescent singlet state has been investigated intensively since the first reports of organic electroluminescence, research into the properties of the phosphorescent triplet state has intensified mainly during the last decade. In this review we give an overview on the photophysical processes associated with the formation of triplet states and their decay, as well as the energy levels and energy transfer processes of triplet states. We aim to give a careful introduction for those new to this particular research area as well as to highlight some of the current research issues and intriguing questions for those familiar with the field. The main focus of this review is on molecular assemblies and polymer films, though relevant work on molecular crystals is also included where it assists in forming a larger picture.