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I don't know of such a survey, but a number of important properties are established in D.W.Barnes, Some theorems on Leibniz algebras, Comm. In Alg. 39, 2463-2472, (2011), and D. W. Barnes, On Levi’s theorem for Leibniz algebras, Bull. Aust. Math. Soc. 86, 184-185, (2012).