Plant branching is a complex and strictly regulated developmental process that significantly affects plant morphogenesis and yield, making it one of the focal points in the study of ideal plant architecture. The formation of plant branches requires at least two critical steps: the formation of axillary meristems and the formation and development of axillary buds into branches. In recent years, it has been confirmed that various factors regulate these processes, ultimately affect the number of plant branches. This article briefly describes the molecular regulatory mechanisms of plant branching, including the regulatory networks of key genes involved in the formation of axillary meristems and the formation and growth of axillary buds. It reviews the effects of various endogenous hormones, including auxins, cytokinins, gibberellins, brassinosteroids, and strigolactones, as well as the nutrient sucrose and environmental factors such as light on branch formation. The aim is to lay the foundation for breeding high-yield new varieties with ideal plant architecture. Additionally, the article discusses the regulatory effects of interactions between hormones on branch formation and analyzes the current state and future directions of research on the branching of oil crops, with the hope of providing a theoretical basis for shaping ideal plant types.