A large amount of diversity of architectural form is found among flowering plants, and an important aspect of this diversity is the wide variation, ranging from simple to complex, found among branching patterns in plant shoot systems. Historically, the control of bud outgrowth has been attributed to the presence of a growing shoot apex. The term "apical dominance" is used to indicate that the shoot tip exerts an inhibitory control over proximal axillary buds. Through decapitation and/or hormone manipulation experiments, this inhibition has been attributed to the phytohormones auxin and cytokinin. Recent studies with mutants demonstrating increased branching indicate important additional roles for organs apart from those in the shoot tip and for signals other than cytokinin and auxin. This chapter provides a critical review of branching with an emphasis toward bud outgrowth in a developmental context. This review provides a detailed synopsis of physiological, genetic, and molecular studies and approaches for the investigation of branching regulation in plants.