In this paper, we review recent progress on space division multiplexed (SDM) transmission and our proposal of dense SDM (DSDM) with more than 30 spatial channels toward capacities beyond petabit/s. Furthermore, we discuss the requirements for realizing long-haul DSDM transport systems using multicore and/or multimode fiber, including power and space efficient amplification schemes, the use of fibers with large effective areas and transmission lines with low intercore crosstalk, low differential mode delay (DMD), and low mode dependent loss (MDL). Graded index heterogeneous 12-core × 3-mode fiber with low crosstalk, low DMD, and low MDL, parallel multiple-input and multiple-output signal processing, low mode dependent gain Erbium-doped fiber amplifiers, and MDL equalization technologies are significant as regards extending the reach of multicore and multimode transmission. We review our long-distance transmission experiment on polarization-division multiplexed 16-quadrature amplitude modulation signaling over 12-core × 3-mode fiber.