The past ten years have seen the rapid expansion of the field of biohybrid robotics. By combining engineered, synthetic components with living biological materials, new robotics solutions have been developed that harness the adaptability of living muscles, the sensitivity of living sensory cells, and even the computational abilities of living neurons. Biohybrid robotics has taken the popular and scientific media by storm with advances in the field, moving biohybrid robotics out of science fiction and into real science and engineering. So how did we get here, and where should the field of biohybrid robotics go next? In this perspective, we first provide the historical context of crucial subareas of biohybrid robotics by reviewing the past 10+ years of advances in microorganism-bots and sperm-bots, cyborgs, and tissue-based robots. We then present critical challenges facing the field and provide our perspectives on the vital future steps towards creating autonomous living machines.