Due to its promising applications in domains like quantum computation or low-power design, synthesis of reversible circuits has become an intensely studied topic. However, many synthesis methods are limited by non-scalable function representations like truth tables. As an alternative, synthesis exploiting graph-based representations have been suggested. The underlying structure is a decision diagram (DD) that may vary regarding reduction methods, decomposition rules, or ordering restrictions. In this work, we review the progress of DD-based synthesis. It is shown that dedicated transformation rules can be applied to generate circuits for functions with a large number of inputs. We discuss the effect of different decomposition types or typical DD improvements like complement edges and re-ordering. Furthermore, we describe how DD-based synthesis can be exploited to transfer theoretical results known from decision diagrams into the domain of reversible circuits. Finally, further directions for future work are outlined.
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