Transport networks such as blood vessel systems and leaf venation are universally required for large-size living organisms in order to overcome the low efficiency of the diffusion in large scale mass transportation. Despite substantial differences in living organisms, such networks have many common patterns — viz. biological transport networks are made up of tubes and flows in tubes deliver target substances. Besides, these networks maintain a tree-like backbone attached with small loops. Experimental and mathematical studies show many similarities in biological mechanisms, which drive structural optimisation in biological transport networks. It is worth noting that the structural optimisation of transport networks in living organisms is achieved in the sense of energy cost as a consequence of natural selection. In this review, we recall the exploration history and show mathematical structures used in the design of biological transport networks.