Brief history of the search for critical structures in heavy-ion collisions

The paper briefly presents history, status, and plans of the search for the critical structures - the onset of fireball, the onset of deconfinement, and the deconfinement critical point - in high energy nucleus-nucleus collisions. First, the basic ideas are introduced, the history of the observation of strongly interacting matter in heavy ion collisions is reviewed, and the path towards the quark-gluon plasma discovery is sketched. Then the status of the search for critical structures is discussed - the discovery of the onset of deconfinement, indications for the onset of fireball, and still inconclusive results concerning the deconfinement critical point. Finally, an attempt to formulate priorities for future measurements - charm quarks vs the onset of deconfinement and detailed study of the onset of fireball - closes the paper.