Autonomous discovery and direct instruction are two extreme sources of learning in children, but educational sciences have shown that intermediate approaches such as assisted discovery or guided play resulted in better acquisition of skills. When turning to Artificial Intelligence, the above dichotomy can be translated into the distinction between autonomous agents, which learn in isolation from their own signals, and interactive learning agents which can be taught by social partners but generally lack autonomy. In between should stand teachable autonomous agents: agents that learn from both internal and teaching signals to benefit from the higher efficiency of assisted discovery processes. Designing such agents could result in progress in two ways. First, very concretely, it would offer a way to non-expert users in the real world to drive the learning behavior of agents towards their expectations. Second, more fundamentally, it might be a key step to endow agents with the necessary capabilities to reach general intelligence. The purpose of this paper is to elucidate the key obstacles standing in the way towards the design of such agents. We proceed in four steps. First, we build on a seminal work of Bruner to extract relevant features of the assisted discovery processes happening between a child and a tutor. Second, we highlight how current research on intrinsically motivated agents is paving the way towards teachable and autonomous agents. In particular, we focus on autotelic agents, i.e. agents equipped with forms of intrinsic motivations that enable them to represent, self-generate and pursue their own goals. We argue that such autotelic capabilities from the learner side are key in the discovery process. Third, we adopt a social learning perspective on the interaction between a tutor and a learner to highlight some components that are currently missing to these agents before they can be taught by ordinary people using natural pedagogy. Finally, we provide a list of specific research questions that emerge from the perspective of extending these agents with assisted learning capabilities.