This perspective paper examines biodesign pedagogy in higher education, focusing on the integration of plant sciences with design and technology. We propose a dual framework for teaching biodesign: nature-driven and socially driven approaches. The nature-driven approach draws inspiration from biological strategies or biotechnologies to address environmental and societal challenges, while the socially driven approach begins with identifying societal problems and exploring biological solutions. Drawing on seven years of teaching experience, we highlight student-led projects that illustrate each approach, including eco-friendly textiles derived from plant fibres and genetically engineered crops designed for sustainable urban agriculture. Our findings underscore the potential of biodesign to bridge STEM and creative disciplines, fostering interdisciplinary collaboration, enhancing scientific literacy and equipping students to tackle complex real-world challenges.