Our understanding of black hole accretion seems to be in pretty good shape. Magnetohydrodynamic simulations have shown that MRI really can drive accretion, and many other observable phenomena besides, and gives rough scaling relations that are closer to the prescient α-model of Shakura and Sunyaev  than we had any right to expect. On the other hand, exquisite observations of time-dependence and spectral transformations in XRBs, and completely new regimes of black hole accretion in TDEs and GRBs, show that the phenomenology of black hole accretion is even richer than we thought.
MHD simulations have come into their own as mature laboratory tools. Shearing-box experiments have been crucial but are probably approaching the end of their useful life. Global simulations — which at the very least are essential for understanding the coupling of disks to winds — have begun to take their place, but do not yet have adequate dynamic range. This is presumably just a matter of computer speed and available CPU time. We will also need to incorporate microphysical effects, such as viscosity, resistivity and heat conduction, which appear to be important for regulating the level of MRI-driven turbulence and perhaps its coupling to large-scale dynamos. On small turbulent scales, the relevant microphysical effects are likely to be collisional, but we will also need codes that can identify current sheets on large scales and compute the collisionless reconnection that is likely to occur.  Finally, the increasing importance of radiation-dominated flows, with luminosities approaching or even greatly exceeding the Eddington limit, means that radiation magnetohydrodynamic codes will be essential. Given the likely role of radiation pressure in driving some of the fastest jets, these codes will have to do radiative transfer in regimes where simple closure schemes are likely to fail.
Not all of these tools are in place yet, but there is every likelihood that these advances will happen soon.
I thank Prof. Phil Armitage for numerous conversations, both over beers and above treeline, and for preparing the figures. My research on black hole accretion and its manifestations is supported in part by National Science Foundation grant AST 1411879, NASA Astrophysics Theory Program grants NNX11AE12G and NNX14AB375, and Department of Energy grant DE-SC008409.