We show that aperiodic superlattices exhibit intriguing interplay between phononic coherent wave interference effects and incoherent transport. In particular, broadband Anderson localization results in a drastic thermal conductivity reduction of 98% at room temperature, providing an ultralow value of 1.3 W m^{-1} K^{-1}, and further yields an anomalously large thermal anisotropy ratio of ∼10^{2} in aperiodic Si/Ge superlattices. A maximum in the thermal conductivity emerges as an unambiguous consequence of phonon Anderson localization at a system length scale bridging the extended and localized transport regimes. The frequency-resolved picture, combined with our lattice dynamical description of Anderson localization, elucidates the rich transport characteristics in these systems and the potential of correlated disorder for sub- to few-THz phononic engineering of heat transport in thermoelectric applications.