Biological materials have been used in construction for as long as we have used wood and limestone; however, biotechnologies seem to offer the potential to grow materials to our specifications and even to allow complex structures to be self-assembled through biological processes. Several promising materials have been identified, including microbially induced calcium carbonate as a cement or mycelium grown on waste materials, which has potential as a structural or insulation material. These developments run parallel to a speculative design discourse – in which features future cities are grown, kept living and self-adapt – as well as research into engineered living materials (ELMs), at the cutting edge of material science and synthetic biology research into ELMs. This question invites a wide range of research contributions in which we identify, evaluate and speculate on the role that grown materials and structures will have on the future of construction. We invite not only experimental work on the latest method in this area but also critique and reflection beyond the ‘hype’ of these, potentially transformative, technologies and approaches.