  As part of a chapter for a book titled "50 years of the renormalization
group", dedicated to the memory of Michael E. Fisher, edited by Amnon Aharony,
Ora Entin-Wohlman, David Huse, and Leo Radzihovsky, I review a class of novel
ordered states of "critical matter", that exhibit strongly fluctuating
universal power-law orders, controlled by an infra-red attractive, non-Gaussian
fixed point. I will illustrate how RG methods pioneered by Wilson and Fisher
can be used to deduce critical phenomenology of such critical phases,
resembling that of a critical point of second order phase transitions, but
requiring no fine tuning.
