Co-development of action, conceptualization and social interaction mutually scaffold and support each other within a virtuous feedback cycle in the development of human language in children. Within this framework, the purpose of this article is to bring together diverse but complementary accounts of research methods that jointly contribute to our understanding of cognitive development and in particular, language acquisition in robots. Thus, we include research pertaining to developmental robotics, cognitive science, psychology, linguistics and neuroscience, as well as practical computer science and engineering. The different studies are not at this stage all connected into a cohesive whole; rather, they are presented to illuminate the need for multiple different approaches that complement each other in the pursuit of understanding cognitive development in robots. Extensive experiments involving the humanoid robot iCub are reported, while human learning relevant to developmental robotics has also contributed useful results.Disparate approaches are brought together via common underlying design principles. Without claiming to model human language acquisition directly, we are nonetheless inspired by analogous development in humans and consequently, our investigations include the parallel codevelopment of action, conceptualization and social interaction. Though these different approaches need to ultimately be integrated into a coherent, unified body of knowledge, progress is currently also being made by pursuing individual methods.