At the intersection of synthetic biology and materials science, the field of engineered living materials (ELMs) has evolved into a new, standalone discipline. The fusion of bioengineering's design-build-test-learn approaches with classical materials science has yielded breakthrough innovations in the synthesis of complex, biologically active materials for functional applications in therapeutics, electronics, construction, and beyond. However, the transdisciplinary nature of the ELM field - and its rapid growth - has made holistic comprehension of achievements related to the tools, techniques, and applications of ELMs difficult across disciplines. To this end, this review proposes an emergent taxonomy of ELM research and uses the categorization to discuss current trends and state-of-the-art advancements, significant opportunities, and imminent challenges for scientists and engineers in the field.