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](https://www.tandfonline.com/doi/abs/10.1080/00927872.2010.489529), Comm. In Alg. 39, 2463-2472,
(2011) ([MSN](https://mathscinet.ams.org/mathscinet-getitem?mr=2821724)), and
D. W. Barnes, [On Levi’s theorem for Leibniz algebras](https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/on-levis-theorem-for-leibniz-algebras/048FA86D849F1552EB9D4F4B93A12AA6), Bull. Aust. Math. Soc. 86,
184-185, (2012) ([MSN](https://mathscinet.ams.org/mathscinet-getitem?mr=2979978)).