The rising complexity and data generation in cyber-physical systems and the Internet of Things require a shift towards an edge-to-cloud computing continuum ecosystem with enhanced artificial intelligence (AI) capabilities. Furthermore, resource limitations and the projected doubling of the electricity used by information and communication technologies until 2030 require innovative resource-efficient solutions. Neuromor-phic computing and intelligence are prominent examples that take inspiration from the function of brains, the most energy-efficient processors known. However, neuromorphic systems differ from conventional von Neumann computers and clock-driven sensor systems and likely require different continuum-enabling abstractions and concepts for large-scale and high-utility neuromorphic systems integration. This paper focuses on communication aspects and summarises recent developments in this area, including a problem analysis aiming to identify challenges and open issues for integrating neuromorphic systems in the digital continuum. Our main contribution is a description of event- and query-based communication models commonly used in microservice architectures, with mappings to defining characteristics of neuromorphic systems and the continuum. In this, we outline an abstraction where each neuromorphic system has a digital counterpart called a Gemi. A Gemi keeps an abstract digital model of its corresponding neuromorphic system, is programmable, and provides digital interfaces. Spike and temporal embedding representations in the neuromorphic systems are mapped to an efficient event-based publish-subscribe model in the digital domain.