The fifth generation (5G) of cellular networks shall host a number of tenants and provide services tailored to meet a wide range of requirements in terms of performance, dependability and security. Network slicing will be a key enabler, by assigning dedicated resources and functionalities to meet such requirements, where the isolation between slices, i.e., that a slice may operate without interference from other slices, becomes a core issue. The objective of this paper is to give a thorough insight into the isolation concept, discuss the challenges involved in providing it, and outline the means available to provide various levels of isolation. Fundamental concepts that can be used in further work to build an isolation solution tailored to ...