My purpose in this paper is to sketch a research direction based on Francisco Varela's pioneering work in neurodynamics (see also Rudrauf et al. 2003, in this issue). Very early on he argued that the internal coherence of every mental-cognitive state lies in the global self-organization of the brain activities at the large-scale, constituting a fundamental pole of integration called here a "dynamic core". Recent neuroimaging evidence appears to broadly support this hypothesis and suggests that a global brain dynamics emerges at the large scale level from the cooperative interactions among widely distributed neuronal populations. Despite a growing body of evidence supporting this view, our understanding of these large-scale brain processes remains hampered by the lack of a theoretical language for expressing these complex behaviors in dynamical terms. In this paper, I propose a rough cartography of a comprehensive approach that offers a conceptual and mathematical framework to analyze spatio-temporal large-scale brain phenomena. I emphasize how these nonlinear methods can be applied, what property might be inferred from neuronal signals, and where one might productively proceed for the future. This paper is dedicated, with respect and affection, to the memory of Francisco Varela.