Research on ionic liquids has achieved rapid progress in the last several decades. Stability is a prerequisite for the application of ionic liquids. Ionic liquids may be used at elevated temperature, as electrolytes, or under irradiation. Therefore, the thermal, electrochemical, and radiolytic stabilities of ionic liquids are important and need to be known before their usage. Many research papers and some reviews on the stabilities of ionic liquids have been published. However, new results are continuously being published and a comprehensive review and perspective on this topic are still urgently needed. In this perspective, we intend to provide a comprehensive review including characterization methods, the effects of chemical composition of the ionic liquids on the thermal, electrochemical, and radiolytic stabilities of ionic liquids, respectively. Moreover, the thermal stability of some special types of ionic liquids such as poly(ionic liquids) and mixed ionic liquids, and the thermal and electrochemical stabilities of protic ionic liquids are discussed too. For thermal stability, the interactions between ions are less important than the individual anions and cations. The decomposition temperature is mainly determined by the less-stable ion, usually the anion. For electrochemical stability, the electrochemical window is determined by both the cation and anion. The less stable ion could influence the stability by interaction between the generated species from the decomposition with the more stable ion (opposite ion). This perspective is helpful for people to avoid using unstable ionic liquids and choose suitable ionic liquids.