Learning Analytics and Multimodal Learning Analytics are changing the way of analysing the learning process while students interact with an educational content. This paper presents a systematic literature review aimed at describing practices in recent Multimodal Learning Analytics and Learning Analytics research literature in order to identify tools and strategies useful for the assessment of the progress and behaviour of children under 6 years old in respect of their learning. The purpose is to provide guidance for Multimodal Learning Analytics research with children under 6 years old to assess their engagement in a task, their emotions, attention, understanding and achievement of a goal. The current state of knowledge on Multimodal Learning Analytics research suggests how performance analytics, face and speech recognition systems, eye tracking, Kinect analytics and wristbands could be used with children. The results show the complexity of collecting data using non-invasive methodologies with children under 6 years old. Ethical implications related to multimodal data from audio, visual, biometric and quantitative measures of child behaviour are discussed.