Controlled drug delivery is a crucial area of study for improving the targeted availability of drugs; several polymer systems have been applied for the formulation of drug delivery vehicles, including linear amphiphilic block copolymers, but with some limitations manifested in their ability to form only nanoaggregates such as polymersomes or vesicles within a narrow range of hydrophobic/hydrophilic balance, which can be problematic. For this, multi-arm architecture has emerged as an efficient alternative that overcame these challenges, with many interesting advantages such as reducing critical micellar concentrations, producing smaller particles, allowing for various functional compositions, and ensuring prolonged and continuous drug release. This review focuses on examining the key variables that influence the customization of multi-arm architecture assemblies based on polycaprolactone and their impact on drug loading and delivery. Specifically, this study focuses on the investigation of the structure–property relationships in these formulations, including the thermal properties presented by this architecture. Furthermore, this work will emphasize the importance of the type of architecture, chain topology, self-assembly parameters, and comparison between multi-arm structures and linear counterparts in relation to their impact on their performance as nanocarriers. By understanding these relationships, more effective multi-arm polymers can be designed with appropriate characteristics for their intended applications.