Petroleum exploration in deep water settings is resulting in the discovery of many giant fields in reservoirs that accumulated in large channel systems on the continental slope. The architecture of these reservoirs is exceedingly complex. In the face of multi-billion dollar costs, it is more important than ever before to accurately characterize these reservoirs. Based on detailed examination of turbidite channel analogs as revealed in 3D seismic data, exposed in outcrops, or preserved on the modern sea floor, two principal models of channel architecture have emerged: a cut-and-fill model, and a lateral accretion model. Both models are appropriate in at least some cases, but debate continues as to which model is most applicable in any specific case. Furthermore, it is not apparent how to reconcile the preserved facies distributions of turbidite channel deposits and prevailing concepts of turbulent flow behavior. For example, when high levees are present, we know that flows are thick. Concentration of sand within sinuous channel elements confirms that turbulent flows are highly stratified. However, these architectures seem to require that the lower and upper portions of a single flow follow paths with markedly different sinuosities and divergent, even opposing, trajectories. How can that happen? Further debate concerns the transition from channel to fan architectures. Some high resolution 3D seismic images suggest the presence of distinct distributary systems on some submarine fans while others do not. Outcrop examples with the best continuous lateral exposures appear to be incompatible with seismic images of distributary systems. The few excellent outcrop examples of lobes arguably are strongly biased. Are our best images from 3D seismic also biased? High resolution images of modern submarine fans calibrated to sediment cores might provide the answer, but such data are lacking. This quandary is not just academic. It has become clear from recent drilling in the Gulf of Mexico that reservoir quality in submarine fans is highly variable, often containing good permeability within channels in contrast to abundant argillaceous sands with low permeability in the lobes. With continued research, the issues discussed above will be resolved, but the path forward, like the channels themselves, will be long and sinuous.