Neurons underpin cognition in animals. However, the roots of animal cognition are elusive from both mechanistic and evolutionary standpoints. Two conceptual frameworks both highlight and promise to address these challenges. First, we discuss evidence that animal neural and other integrative systems evolved more than once (convergent evolution) within basal metazoan lineages, giving us unique experiments by Nature for future studies. The most remarkable examples are neural systems in ctenophores and neuroid-like systems in placozoans and sponges. Second, in addition to classical synaptic wiring, a chemical connectome mediated by hundreds of signal molecules operates in tandem with neurons and is the most information-rich source of emerging properties and adaptability. The major gap—dynamic, multifunctional chemical micro-environments in nervous systems—is not understood well. Thus, novel tools and information are needed to establish mechanistic links between orchestrated, yet cell-specific, volume transmission and behaviors. Uniting what we call chemoconnectomics and analyses of the cellular bases of behavior in basal metazoan lineages arguably would form the foundation for deciphering the origins and early evolution of elementary cognition and intelligence.