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Dual learning has been successfully applied in many machine learning applications including machine translation, image-to-image transformation, etc. The high-level idea of dual learning is very intuitive: if we map an $x$ from one domain to another and then map it back, we should recover the original $x$. Although its effectiveness has been empirically verified, theoretical understanding of dual learning is still very limited. In this paper, we aim at understanding why and when dual learning works. Based on our theoretical analysis, we further extend dual learning by introducing more related mappings and propose multi-step dual learning, in which we leverage feedback signals from additional domains to improve the qualities of the mappings. We prove that multi-step dual learn-ing can boost the performance of standard dual learning under mild conditions. Experiments on WMT 14 English$\leftrightarrow$German and MultiUNEnglish$\leftrightarrow$French translations verify our theoretical findings on dual learning, and the results on the translations among English, French, and Spanish of MultiUN demonstrate the effectiveness of multi-step dual learning.