Tiny machine learning (tinyML) is a fast-growing and emerging field at the intersection of machine learning (ML) algorithms and low-cost embedded systems. It enables on-device analysis of sensor data (vision, audio, IMU, etc.) at ultra-low-power consumption (<1mW). Moving machine learning compute close to the sensor(s) allows for an expansive new variety of always-on ML use-cases, especially in size, weight and power (SWaP) constrained robots. This talk introduces the broad vision behind tinyML, and specifically, it focuses on exciting new applications that tinyML enables for cheap and lightweight on-device robot learning. Although tinyML for robotics has rich possibilities, there are still numerous technical challenges to address. Tight onboard processor, memory and storage constraints, coupled with embedded software fragmentation, and a lack of relevant large-scale tinyML sensor datasets and benchmarks pose a substantial barrier to developing novel robotics applications. To this end, the talk touches upon the myriad research opportunities for unlocking the full potential of "tiny robot learning," spanning from algorithm design to automatic hardware synthesis.