The thin disk regime of accretion, where the accretion rate is neither too high as to exceed the Eddington limit, nor too low as to lead to radiative inefficiency, is often considered to be the simplest and best-understood case. It applies to many AGN and to the luminous states of X-ray binaries. Quantitative comparisons of thin disk theory to observations, however, are often found lacking. In this talk, I will argue that the properties of radiatively efficient accretion disks are dramatically modified in the presence of relatively weak net magnetic fields. Simulations suggest that disks in which the magnetic pressure becomes comparable to the gas or radiation pressure look very different from their weakly magnetized counterparts. Speculation points to a possible scenario in which the observable characteristics of black hole accretion are largely byproducts of how the magnetic flux threading the disk evolves over time.