In this paper, we attempt to find a unified framework in which the statistics of wave propagation in random media can be understood as strengths of scattering and absorption increase. First, we discuss the weak scattering, diffusive limit without absorption. In this limit, the suppression of transmission by weak localization, the distribution of total transmission and the intensity correlation functions with displacement and polarization rotation are all described in terms of the dimensionless conductance so that these effects are explicitly linked. When absorption is introduced, the dimensionless conductance can no longer serve as a fundamental scaling parameter, but the variance of the total transmission is still able to chart the changing statistical character of propagation and localization with sample size. By examining transport at a fixed time following pulsed excitation, the affect of absorption can be removed while the growing impact of localization can be clearly discerned. The functional form of probability distributions of intensity and total transmission and of the spatial and polarization intensity correlation functions in the time domain are the same as in the frequency domain. The connection of mesoscopic fluctuations to localization can be seen in the spectral correlation function of the field, which is the Fourier transform of average pulsed transmission. The spectral field correlation function can be expressed as a product of the correlation function of the field normalized to the average amplitude in a given configuration and of the square root of the total transmission.