<p>People use hundreds of words to describe emotions and related mental states. Yet a large psychological literature and our own intuition argue for a simpler structure that underlies these attributions, since most of the words are antonyms or synonyms that map onto a few basic dimensions or categories. However, there is surprisingly little agreement on their number or interpretation: core affect is generally thought to be two-dimensional; emotion categories vary from six to over twenty; and according to some theories emotion concepts are much higher dimensional since they flexibly incorporate context. Although many of these debates originate in theoretical disagreements, we here focus on methodological sources: how stimuli are selected, tasks are chosen, and dimensionality reduction algorithms are used. We provide a survey of popular methods, their advantages and limitations, and recommendations for best practices.</p>