In this paper, we describe recent progress in space-division multiplexed (SDM) transmission, and our proposal and demonstration of dense space-division multiplexing (DSDM), which offers the possibility of ultra-high capacity SDM transmission systems with high spatial density and spatial channel count of over 30 per fiber. We introduce the SDM transmission matrix, which cross indexes the various types of multi-core multi-mode transmissions according to the type of light propagation in optical fibers and how the spatial channels are handled in the network. For each category in the matrix, we present the latest advances in transmission studies, and evaluate their transmission performance by spectral and spatial efficiencies. We also expound on technologies for multi-core and/or multi-mode transmission including optical fiber, signal processing, spatial multi/demultiplexer, and amplifier, which will play key roles in configuring DSDM transmission systems, and review the first DSDM transmission experiment over a 12 core x 3 mode fiber.