The phase transition of an ion beam into its crystalline state has long been expected to dramatically influence beam dynamics beyond the limitations of standard accelerator physics. Yet, although considerable improvement in beam cooling techniques has been made, strong heating mechanisms inherent to existing high-energy storage rings have prohibited the formation of the crystalline state in these machines up to now. Only recently, laser cooling of low-energy beams in the table-top rf quadrupole storage ring PAaul Laser cooLing Acceleration System (PALLAS) has lead to the experimental realization of crystalline beams. In this article, the quest for crystalline beams as well as their unique properties as experienced in PALLAS will be reviewed.