Abstract Common mycorrhizal networks (CMNs) are an enigmatic feature of soil and mycorrhizal ecology. The current use of the term ‘common mycorrhizal network’ stipulates a direct, continuous physical link between plants formed by the mycelium of mycorrhizal fungal genets. This means that a specific case (involving hyphal continuity) is used to define a much broader phenomenon of hyphae interlinking among roots of different plants. We here embrace a more inclusive definition of the CMN as a network formed by mycorrhizal fungal genets among roots of different plants, irrespective of the type of connection or interaction, and not limited to direct hyphal linkages. Implicitly, this broader version of the term has been used by many researchers already. We propose using the term ‘common mycorrhizal networks with hyphal continuity’ (CMN‐HC) to capture the more specific case of a continuous link via hyphae between the roots of different plants, which is important to study for some (notable carbon and nutrient exchange), but not all functions of a CMN (e.g. transfer of infochemicals or microbes). In addition, and becoming more general than CMN, we introduce the term ‘common fungal network’ (CFN) to include networks of any type of connection formed between different plants by any type of fungus; this includes also non‐mycorrhizal fungi, and indeed a combination of non‐mycorrhizal and mycorrhizal networks. We assert that this new conceptual framework incorporating three hierarchical terms (CMN‐HC, CMN and CFN), ranging from the most specific to the very broad, can usher in a period of new research activity on fungal networks. Read the free Plain Language Summary for this article on the Journal blog.