  This Colloquium reviews the 25 year quest for understanding the continuous
(second-order) mean-field-like phase transition occurring at 17.5 K in URu2Si2.
About ten years ago, the term hidden order (HO) was coined and has since been
utilized to describe the unknown ordered state, whose origin cannot be
disclosed by conventional solid-state probes, such as x rays, neutrons, or
muons. HO is able to support superconductivity at lower temperatures (Tc ~ 1.5
K), and when magnetism is developed with increasing pressure both the HO and
the superconductivity are destroyed. Other ways of probing the HO are via
Rh-doping and very large magnetic fields. During the last few years a variety
of advanced techniques have been tested to probe the HO state and their
attempts will be summarized. A digest of recent theoretical developments is
also included. It is the objective of this Colloquium to shed additional light
on the HO state and its associated phases in other materials.
