The Microscale Robotics Laboratory at the BioRobotics Institute of Scuola Superiore Sant'Anna aims at developing advanced robotic technologies with sub-millimetre dimensions. Our approach is based on bioinspiration, as we look at cells for the design of microrobots with advanced mobility and navigation abilities. In particular, we aim at translating the mechanisms that drive cellular motility into new designs of artificial mobile microrobots, and at realizing microrobotic models for testing hypothesis on specific behaviours in cells (e.g. for studying cells locomotion and migration in body tissues). By leveraging on bioinspired designs, we address fundamental limitations of current microrobots and develop innovative microrobotic technologies with high potential impact in minimally invasive medicine. In particular, we aim at endowing microrobots with advanced robotics capabilities (i.e. autonomy), resulting in a totally new level of functionality that will enable currently unforeseen medical application scenarios. In the endeavour towards advanced autonomous microrobots, we also address the emergence of intelligent behaviours in microscale physical systems. Our microrobots will rely on the physical and chemical interaction with the environment, and complex behaviours will emerge (in a predictable and programmable way) from the complex interplay of the reactions of their constitutive materials to the environments. This will pave the way towards a transformative bottom-up approach for robotics and embodied intelligent systems.