The kidney develops as an outgrowth of the epithelial nephric duct known as the ureteric bud, in a position specified by a range of rostral and caudal factors which serve to ensure two kidneys form in the appropriate positions in the body. At its simplest level, kidney development can be viewed as the process by which this single bud then undergoes a process of arborisation to form a complex connected network of ducts which will serve to drain urine from the nephrons in the adult organ. The process of bud elaboration is dictated by factors expressed by both the bud itself and by surrounding cells of the metanephric mesenchyme which control cell division and bifurcation. These cells play two critical roles. Firstly, they potentiate the ongoing elaboration of the ureteric tree: remove them and branching ceases. Secondly, they harbour progenitor cells which are fated to undergo their own process of tubulogenesis to form the nephrons of the adult organ. In this chapter, we will discuss how the ureteric bud arises in the developing embryo, how it undergoes branching, how we can measure and study this process and finally the likely relevance that this process has for our understanding of congenital and acquired kidney disease.