The optical fibre is an essential tool for our communication infrastructure since it is the main transmission channel for optical communications. The latest major advance in optical fibre technology is space-division multiplexing, where new fibre designs and components establish multiple co-existing data channels based on light propagation over distinct transverse optical modes. Simultaneously, there have been many recent developments in the field of quantum information processing, with novel protocols and devices in areas such as computing and communication. Here, we review recent results in quantum information based on space-division multiplexing optical fibres, and discuss new possibilities based on this technology.