We discuss the role of geometry and topology in reasoning processes related to wireless and wired communication networks. We focus especially on future research directions on enabling autonomic reasoning taking place within the networks themselves. This work is a part of our ongoing effort to better understand future “cognitive communication systems” that are likely to employ various adaptive techniques, also borrowing from artificial intelligence research community to optimise their behaviour in an automated manner. As the field is very young, we mainly attempt to succinctly review and organize the state-of-the-art, and identify areas in which further research is urgently needed.