We share our thoughts with other minds, but we do not understand how. Having a common language certainly helps, but infants’ and tourists’ communicative success clearly illustrates that sharing thoughts does not require signals with a pre-assigned meaning. In fact, human communicators jointly build a fleeting conceptual space in which signals are a means to seek and provide evidence for mutual understanding. Recent work has started to capture the neural mecha- nisms supporting those fleeting conceptual alignments. The evidence suggests that communicators and addressees achieve mutual understanding by using the same computational procedures, implemented in the same neuronal sub- strate, and operating over temporal scales independent from the signals’ occurrences.