Designing stable π-radicals

π-Conjugated radicals, molecules with unpaired electrons, have been known since Gomberg's discovery of the persistent triphenylmethyl in 1900. First considered a curiosity, π-radicals have helped to refine the electronic structure theory and better understand the reactivity of organic compounds, and for the last 40 years have been actively pursued as functional materials: single component organic conductors, semiconductors for field-effect transistors, organic magnets, and most recently, as electroluminescent and quantum materials. This tutorial review provides the essential quantum-chemical background and practical lessons learned from 125 years of the history of developing stable π-radicals, aiming to inspire and inform new researchers entering this field. We discuss the cause of the reactivity of π-radicals and the methods to suppress this reactivity in the design of stable π-radicals. Without any intent of comprehensive coverage, we systematise and highlight the most important examples of stable neutral π-radicals, covering arylmethyl, polycyclic hydrocarbon, conjugated heteroatomic radicals, di- and polyradicals while also briefly covering radical ions. We show how the presence of unpaired electrons in these molecules is manifested in their unusual electronic, optical and magnetic properties, and summarise the most important applications of π-radicals explored to date. Our overall goal is to bring the accumulated knowledge of the field to the attention of a new generation of researchers designing stable π-radicals in pursuit of various applications.