Luminescent waveguides (LWs) occur in a wide range of applications, from solar concentrators to doped fiber amplifiers. Here we report a comprehensive analysis of escape-cone losses in LWs, which are losses associated with internal rays making an angle less than the critical angle with a waveguide surface. For applications such as luminescent solar concentrators, escape-cone losses often dominate all others. A statistical treatment of escape-cone losses is given accounting for photoselection, photon polarization, and the Fresnel relations, and the model is used to analyze light absorption and propagation in waveguides with isotropic and orientationally aligned luminophores. The results are then compared to experimental measurements performed on a fluorescent dye-doped poly(methyl methacrylate) waveguide.