Fast magnetic reconnection events can play an important role in accretion disk systems. A potential model to explain the non-thermal very-high-energy (VHE) emission (from GeV to TeV) observed in black-hole binaries (BHBs) and Active Galatic Nuclei (AGNs) can be attributed to fast magnetic reconnection induced in the turbulent corona of accretion disks and/or jets. In this work, we will discuss the results of global general relativistic MHD (GRMHD) simulations of accretion disks around black holes, whose turbulence is naturally driven by MHD instabilities, such as the magnetorotational instability (MRI). We will also present studies of magnetic reconnection driven by kink instabilities inside jets employing special relativistic MHD (SRMHD) simulations. As we expect, our simulations reveal the development of a nearly steady-state turbulence driven by these instabilities. We have performed a detailed statistical analysis to identify the presence of current sheets in the turbulent regions of both the accretion flow and jet. We then determined the magnetic reconnection rates in these locations obtaining average reconnection velocities in Alfvén speed units of the order of $0.01-0.7$, which are consistent with the predictions of the theory of turbulence-induced fast reconnection.