The capacity of optical transmission systems has increased dramatically since their first deployments in the mid 1970s . However, studies show that the theoretical capacity limit of single-mode fiber is about to be reached, and space-division multiplexing has been proposed to overcome this limit. With the high levels of integration needed for economic deployment, space-division multiplexing may exhibit large crosstalk between the supported fiber modes. We propose to use coherent multiple-input multiple-output (MIMO) digital signal processing (DSP), a technique widely used in wireless communication, to compensate crosstalk present in spatial multiplexing over fibers. According to MIMO theory, crosstalk in multi-mode transmission systems can be completely reversed if the crosstalk is described by a unitary transformation. For optical fibers this is fulfilled if all available fiber modes can be selectively excited and if all the modes are coherently detected at the end of the fiber, provided that mode-dependent loss is negligible. We successfully applied the technique to demonstrate the transmission of six independent mode-multiplexed 20-Gbaud QPSK signals over a single, optically amplified span of 137-km few-mode fiber (FMF). Further, in a multi-span experiment, we reach 1200 km by transmitting over a 3-core coupled-core fiber (CCF). Details for both experiments will be presented, including the description of the supported polarization-and spatial modes of the fiber, the mode multiplexers used to launch and detect the modes, and the MIMO DSP algorithm used to recover the channels.