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).