A thorough millimeter-wave measurement campaign is carried out in an indoor environment with an aim at characterizing the short-term fading channel behavior. The measurements are conducted in a variety of scenarios, with frequencies ranging from 55 GHz to 65 GHz, in lineof-sight and non-line-of-sight conditions, and combinations of horizontal and vertical polarizations at both transmitter and receiver. A number of fading models are tested, namely Rayleigh, Rice, Nakagami-m, α-μ, κ-μ, η-μ, and α-η-κ-μ. The statistics under analysis are those characterizing the fading amplitude and the frequency selectivity. In particular, the probability density and cumulative distribution functions for the former and level crossing rate per bandwidth unit for the latter are the respective first- and second-order statistics used. To this end, from the experimental data, the parameters of the models are estimated and the corresponding theoretical curves are plotted and compared with the empirical ones. Whereas the required theoretical formulations of the first-order statistics of these models are already well known, those of the second-order statistics as well as these fitting process in such a band shown here are unprecedented in the literature.