The great demand for tissue and organ grafts, compounded by an ageing demographic and a shortage of available donors, has driven the development of bioengineering approaches that can generate biomimetic tissues in vitro. Despite the considerable progress in conventional scaffold-based tissue engineering, the recreation of physiological complexity has remained a challenge. Bottom-up tissue engineering strategies have opened up a new avenue for the modular assembly of living building blocks into customized tissue architectures. This Progress Report will overview the recent progress and trends in the fabrication and assembly of living building blocks, with a key highlight on emerging bioprinting technologies that can be used for modular assembly and complexity in tissue engineering. By summarizing the work to date, providing new classifications of different living building blocks, highlighting state-of-the-art research and trends, and offering personal perspectives on future opportunities, this Progress Report aims to aid and inspire other researchers working in the field of modular tissue engineering.