Natural biological materials exhibit remarkable properties: self-assembly from simple raw materials, precise control of morphology, diverse physical and chemical properties, self-repair, and the ability to sense-and-respond to environmental stimuli. Despite having found numerous uses in human industry and society, the utility of natural biological materials is limited. But, could it be possible to genetically program microbes to create entirely new and useful biological materials? At the intersection between microbiology, material science, and synthetic biology, the emerging field of biological engineered living materials (ELMs) aims to answer this question. Here we review recent efforts to program cells to produce living materials with novel functional properties, focusing on microbial systems that can be engineered to grow materials and on new genetic circuits for pattern formation that could be used to produce the more complex systems of the future.