The construction of artificial cells from inanimate molecular building blocks is one of the grand challenges of our time. In addition to being used as simplified cell models to decipher the rules of life, artificial cells have the potential to be designed as micromachines deployed in a host of clinical and industrial applications. The attractions of engineering artificial cells from scratch, as opposed to re‐engineering living biological cells, are varied. However, it is clear that artificial cells cannot currently match the power and behavioural sophistication of their biological counterparts. Given this, many in the synthetic biology community have started to ask: is it possible to interface biological and artificial cells together to create hybrid living/synthetic systems that leverage the advantages of both? This article will discuss the motivation behind this cellular bionics approach, in which the boundaries between living and non‐living matter are blurred by bridging top‐down and bottom‐up synthetic biology. It details the state of play of this nascent field and introduces three generalised hybridisation modes that have emerged.