Space division multiplexing (SDM) transmission technology is the prime candidate for next technological breakthrough in fiber-optic communication systems, as spatially structured multicore fibers and multimode fibers allow exploitation of the spatial degrees of freedom. Although the use of multi-input multi-output (MIMO) signal processing has significantly contributed to the development of MIMO-SDM transmission, differential mode delay (DMD) and mode dependent loss (MDL) remain as restricting factors of long-haul MIMO-SDM transmission. This paper starts by reviewing the recent progress demonstrated by SDM transmission experiments. Issues with MIMO-SDM transmission including DMD and MDL are then discussed with their methodologies based on optical and digital approaches. Next, brief descriptions of linear and nonlinear MIMO signal processing techniques that enable robust and reliable MIMO-SDM transmission are provided with complexity and performance comparisons, followed by a discussion of their adaptation in coherent MIMO-SDM transmission. We also elucidate the experimental evaluation of frequency selective channels in a multicore few-mode fiber with experimental evaluations, and discuss their impact on MIMO-SDM signal transmission from a signal processing perspective.