In this talk, I will give some examples of the research we have carried out at KTH Royal Institute of Technology in the past years on modelling different aspects of human language acquisition. The topics we have addressed span from feature extraction and normalization to the acquisition of speech building blocks, such as phonetic classes and words, to the association of those speech units to meaning (grounding). Although the methods proposed here are not necessarily biologically plausible, they are motivated by the goal of addressing the same challenges that human infants face when they learn to understand and produce speech and language. This departs drastically from the usual deployment of machine learning in the context of speech technology. The key aspects are a) learning by imitation rather than from annotations, b) learning with respect to the agent's embodiment, c) learning from multimodal sensory inputs, d) learning actively by interacting with the environment. Additionally, I will cover examples of multimodal human activity recognition and acoustic reasoning.