  We revisit Huber's theory of continuous valuations, which give rise to the
adic spectra used in his theory of adic spaces. We instead consider valuations
which have been reified, i.e., whose value groups have been forced to contain
the real numbers. This yields reified adic spectra which provide a framework
for an analogue of Huber's theory compatible with Berkovich's construction of
nonarchimedean analytic spaces. As an example, we extend the theory of
perfectoid spaces to this setting.
