An excellent and clear review of String Field Theory may be found in the paper "Analytical Solutions of Open String Field Theory" by Ehud Fuchs and Michael Kroyter: hep-th/0807.4722. It discusses the CFT and the Oscillator Formalism for covariant string field theory and presents the Schnabl solutions. There is also a detailed discussion of the Sen conjectures as well.
The following lecture notes by Washington Taylor are also of pedagogical in nature: "Lectures on D-branes, tachyon condensation, and string field theory": hep-th/0301094
The BV formalism for closed string field theory is discussed in the article by Charles B. Thorn if you are interested in that (although I haven't managed to go past the early few sections): "String Field Theory" http://www.sciencedirect.com/science/article/pii/037015738990015X
Carlo Maccaferri has a succinct review of the subject which gives a broad picture and clearly introduces the CFT formalism : Basics of String Field Theory http://www.ulb.ac.be/sciences/ptm/pmif/Rencontres/ModaveII/Carlo.pdf
And if you are interested in the Berkovits formalism for superstring field theory, his own review might be useful (again I haven't studied this paper): "Review of Open Superstring Field Theory" by Nathan Berkovits - hep-th/0105230. He has developed a newer formalism but I can't think of a review article.
Hope these help, thanks!