Network programmability is crucial for addressing the multiplicity and heterogeneity of Network Services, the diversity of the underlying infrastructure of Sixth Generation (6G) communication systems, and the requirements for maximum efficiency. The programmability of a service platform enables algorithmic network management by leveraging contemporary software virtualization technologies. Moreover, network programmability will abstract the essential network/service and resource configuration, as well as the production and administration of policy lifecycles, as the number of local breakouts (both public and private) is anticipated to grow exponentially. Network programmability is the central point of interest for Hexa-X, the European 6G flagship project, which aims to facilitate the dynamic adaptation to changing network situations and requirements for the most efficient use of available resources. To explore such a critical enabler of futuristic mobile networks, this article addresses the role of network and service programmability and its impact on various aspects of 6G within the context of Hexa-X. In order to accomplish this, the article begins by discussing Hexa-X’s proposed service Management and Orchestration (M&O) framework for 6G. Based on this framework, it identifies and explores in greater detail the programmability of four primary processes in 6G: expressing application and service requirements; service description models and profiling; monitoring and diagnostics; and reasoning. Beyond the scope of the Hexa-X, this article aims to serve as a foundation for future research into network and service programmability in 6G.