This paper presents the first comprehensive tutorial on a promising research field located at the frontier of two well-established domains: Neurosciences and wireless communications, motivated by the ongoing efforts to define how the sixth generation of mobile networks (6G) will be. In particular, this tutorial first provides a novel integrative approach that bridges the gap between these two, seemingly disparate fields. Then, we present the state-of-the-art and key challenges of these two topics. In particular, we propose a novel systematization that divides the contributions into two groups, one focused on what neurosciences will offer to 6G in terms of new applications and systems architecture (Neurosciences for Wireless), and the other focused on how wireless communication theory and 6G systems can provide new ways to study the brain (Wireless for Neurosciences). For the first group, we concretely explain how current scientific understanding of the brain would enable new application for 6G within the context of a new type of service that we dub braintype communications and that has more stringent requirements than human- and machine-type communication. In this regard, we expose the key requirements of brain-type communication services and we discuss how future wireless networks can be equipped to deal with such services. Meanwhile, for the second group, we thoroughly explore modern communication system paradigms, including Internet of Bio-nano Things and chaosbased communications, in addition to highlighting how complex systems tools can help bridging 6G and neuroscience applications. Brain-controlled vehicles are then presented as our case study. All in all, this tutorial is expected to provide a largely missing articulation between these two emerging fields while delineating concrete ways to move forward in such an interdisciplinary endeavor.