We analyze coherent wave transport in a new physical setting associated with multimode wave systems where reflection is completely suppressed and mode-dependent losses together with mode mixing are dictating the wave propagation. An additional physical constraint is the fact that in realistic circumstances the access to the scattering (or transmission) matrix is incomplete. We have addressed all these challenges by providing a statistical description of wave transport which fuses together a free probability theory approach with a filtered random matrix ensemble. Our theoretical predictions have been tested successfully against experimental data of light transport in multimode fibers. Recently, the interest in wave transport has extended to new physical settings with practical relevance, namely, a class of complex multimode systems where reflection processes are absent [16,17]. Obviously, the zero reflectivity condition, imposes new constraints to the wave scattering process, thus constituting the previous RMT predictions void. These type of transport problems have emerged naturally in the framework of multimode (or coupled multi-core) fiber optics. In these systems, fiber imperfections (core ellipticity and eccentricity) and external perturbations (index fluctuations and fiber bending) cause coupling and interference between propagating signals in different spatial modes and orthogonal polarizations. At the same time, the effect of mode-dependent loss (MDL) (or gain due to optical amplifiers) in wave propagation is another important feature whose ramifications are not yet completely understood [16][17][18][19]. In the framework of multimode fibers (MMFs), for example, it leads to fundamental limitations in their performance since extremely high MDL can reduce the number of propagating modes and thus the information capacity of MMFs. It is, therefore, imperative to develop statistical theories that take into consideration the modal and polarization mixing and MDL and provide a quantitative description of light transport in realistic MMFs (and other multimode systems that demonstrate similar challenges).