  We review some recent results of general relativistic magnetohydrodynamic
(GR-MHD) simulations considering the evolution of geometrically thin disks
around a central black hole. Thin disk GR-MHD simulations complement the widely
used MAD (Magnetically Arrested Disk) or SANE (Standard And Normal Evolution)
approaches of evolving from an initial disk torus. In particular, we discuss
the dynamical evolution of the disk, its role in the formation of disk winds or
jets, the impact of disk resistivity, and its potential role in generating
magnetic flux by an internal disk dynamo. The main characteristics of a thin
disk in our approach are the Keplerian rotation of the disk material, which
allows to launch disk outflows by the Blandford-Payne magneto-centrifugal
effect, in addition to the Blandford-Znajek-driven spine jet from the black
hole ergosphere. Thus, for this approach, we neglect disk thermodynamics and
radiative effects, concentrating predominantly on the dynamical evolution of
the system. Resistive MHD further allows the investigation of physical
reconnection and also dynamo action. Magnetic reconnection may generate
magnetic islands of plasmoids that are ejected from the disk along with the
outflow. We also discussed potential applications of thin disk in explaining
the decaying phase of an outburst in black hole X-ray binaries (BH-XRBs).
Post-processing of radiation using the simulated dynamical data allows to
derive spectra or fluxes, e.g., in the X-ray band, and to derive potential
variability characteristics.
