Discrete and nondeterministic modelling of regulatory and signalling networks allows to characterize many of their crucial dynamical properties, with a reasonable computational effort. A dynamical feature of particular interest in its own right, as well as in terms of biological relevance, is the landscape of attractors and their attraction basins. In recent years, we have developped new approaches to discovery and global cartography of this basin landscape. We enlarge the set of models used, by moving to Petri nets on the one hand and an opening to continuous dynamics on the other. Surprisingly, these openings are rewarded not only by a sharpening of the analysis, but also the emergence of compact and readable data structures, and fast search algorithms. The talk will advocate the cross-fertilization between discrete and continuous approaches, and to not be afraid of pushing limits.