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A great part of economic literature deals with structural changes, i.e. long-run changes in the structure of economic aggregates. While the standard literature relies on the mathematical branches of analysis and algebra for modeling structural change and describing the relevant empirical evidence, we choose a topological approach, which relies on the notions of self-intersection and mutual intersection of trajectories. We discuss all the methodological and mathematical aspects of this approach and show that it is applicable to a wide range of classical topics and papers of growth and development theory. Then, we apply it for studying a specific type of structural change, namely, the long-run labor re-allocation across sectors: we (a) elaborate new empirical evidence stating that mutual intersection and non-self-intersection are stylized facts of long-run labor re-allocation, (b) suggest and discuss theoretical explanations of non-self-intersection, and (c) discuss mathematical methods for explaining mutual intersection by using standard structural change models. Overall, our approach generates new evidence, new critique points of the previous structural change literature, new theoretical arguments, and a wide range of new research topics.

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