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Structural engineers play an increasing role in ensuring the transition towards a more sustainable construction sector: a) they are responsible for the design of the most resource- and energy-intensive part of buildings and infrastructure, and b) they regularly interact with architects, contractors, and clients, and hence are full stakeholders in the overall decision process. Traditionally, structural engineers follow two paths to reduce structure environmental impacts: 1) minimizing the volume of material, and 2) adopting low impact (e.g. low carbon) materials. A third strategy that has recently re-emerged in practice and research is the reuse of structural components over multiple service cycles, which allows drastically reducing raw material use, reprocessing energy, and waste. Therefore, employing reuse strategies in structural design has considerable potential to reduce structure environmental impacts further. Although reuse is not new, systematic adoption in practice implies an important paradigm shift: rather than manufacturing components after the structural system has been designed, the system must be synthesized from a stock of available components. The first part of our contribution provides an overview of historic and contemporary structures that efficiently reuse structural components. It also highlights the influence of component reuse on the structural design process. The second part presents a new computational tool for the conceptual design of structures from a stock of reclaimed elements. The tool combines Combinatorial Equilibrium Modelling, graphic statics, efficient Best-Fit heuristics, and Life Cycle Assessment to explore different design options in a user-interactive way and with almost real-time feedback. The method applicability is demonstrated through a realistic case study for the design of a complex 3D spatial structure made of reclaimed structural elements originating from deconstructed buildings in Switzerland. Results show that structures made of reused elements have a significantly lower environmental impact than solutions made of new material only. Link to the video: https://youtu.be/VCyD1yqXH8w