This paper examines the role of R{e}nyi entropy in ordering distributions and establishes a relation between R{e}nyi entropy ordering of distributions and a strong ordering known as dispersion ordering. It is also shown that R{e}nyi entropy of continuous transformations behave similar to variance and Shannon entropy. Further, we investigate R{e}nyi entropy ordering of location-scale and shape-scale families. The results are conveniently tabulated in terms of distribution parameters. If a system is known to have survived to age t, then R\'{e}nyi entropy is no longer useful for measuring the uncertainty about the remaining lifetime of a system. Asadi textit{et al.} (2005) defined dynamic R{e}nyi entropy which measures the uncertainty about the remaining lifetime of a system of age t. We present a bound for dynamic R\'{e}nyi entropy of a system in terms of mean residual life function. Then some conditions are stated under which R{e}nyi entropy of a residual lifetime distribution is monotone. We give sufficient conditions for a function phi(X) of a random variable X to have more (less) dynamic R{e}nyi entropy than X itself.

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