Signatures of photon localization are observed in a constellation of transport phenomena which reflect the transition from diffusive to localized waves. The dimensionless conductance, g, and the ratio of the typical spectral width and spacing of quasimodes, \delta, are key indicators of electronic and classical wave localization when inelastic processes are absent. However, these can no longer serve as localization parameters in absorbing samples since the affect of absorption depends upon the length of the trajectories of partial waves traversing the sample, which are superposed to create the scattered field. A robust determination of localization in the presence of absorption is found, however, in steady-state measurements of the statistics of radiation transmitted through random samples. This is captured in a single parameter, the variance of the total transmission normalized to its ensemble average value, which is equal to the degree of intensity correlation of the transmitted wave, \kappa. The intertwined effects of localization and absorption can also be disentangled in the time domain since all waves emerging from the sample at a fixed time delay from an exciting pulse, t, are suppressed equally by absorption. As a result, the relative weights of partial waves emerging from the sample, and hence the statistics of intensity fluctuations and correlation, and the suppression of propagation by weak localization are not changed by absorption, and manifest the growing impact of weak localization with t.