Production of paper-based packaging is growing at the present moment and has great future prospects. However, the development of new packaging concepts is creating a demand for an improvement in the mechanical properties of paper. Extensibility is one of these properties. Highly extensible papers have the potential to replace certain kinds of plastics used in packaging. Extensibility is also important for the sack and bag paper grades and for runnability in any converting process. This paper reviews the factors that affect the extensibility of fibres and paper, and discusses opportunities for improving the straining potential of paper and paper-like fibre networks. It is possible to classify factors that affect extensibility into three main categories: fibre structure, interfibre bonding, and structure of the fibre network. Extensibility is also affected by the straining situation and the phase state of the polymers in the cell wall. By understanding the basic phenomena related to the elongation, and by combining different methods affecting the deformability of fibre network, extensibility of paper can be raised to a higher level.