In this article, we propose a communicative learning (CL) formalism that unifies existing machine learning paradigms, such as passive learning, active learning, algorithmic teaching, and so forth, and facilitates the development of new learning methods. Arising from human cooperative communication, this formalism poses learning as a communicative process and combines pedagogy with the burgeoning field of machine learning. The pedagogical insight facilitates the adoption of alternative information sources in machine learning besides randomly sampled data, such as intentional messages given by a helpful teacher. More specifically, in CL, a teacher and a student exchange information with each other collaboratively to transmit and acquire certain knowledge. Each agent has a mind, which includes the agent's knowledge, utility, and mental dynamics. To establish effective communication, each agent also needs an estimation of its partner's mind. We define expressive mental representations and learning formulation sufficient for such recursive modeling, which endows CL with human-comparable learning efficiency. We demonstrate the application of CL to several prototypical collaboration tasks and illustrate that this formalism allows learning protocols to go beyond Shannon's communication limit. Finally, we present our contribution to the foundations of learning by putting forth hierarchies in learning and defining the halting problem of learning.