Over at the Leiter Law Reports, Brian has posted some excellent items on publishing in law reviews both here and here. For those less familiar, law reviews work very differently than other academic journals.
When submitting a paper to an academic journal, personal information is deleted from the paper. One's qualifications, professional job title, etc. will be of no importance at all. Refereeing is almost always anonymous and double-blind. Referees will be experts in the field from all over the world. Decisions may take at least two months.
Law reviews are entirely different. Many require you provide personal information: one's qualifications, professional job title, etc. may help/hurt chances of publication. Refereeing is not always anonymous and double-blind. The referees are often graduate students studying law at said university law review. (Thus, The University of Chicago Law Review's referees will be graduate students studying law at Chicago's law school.) Because the referees are largely limited to one small pool of students, the norm for authors is to submit to a large number of law reviews at once. This is acceptable because there is no chance that the same pair of eyes will referee the paper for different journals. Decisions can often be quite quick, although perhaps non-existent elsewhere: I have submitted papers to journals that never acknowledged receipt (nor denied it) nor ever made a decision.
The websites above have useful information for anyone looking for more specific advice on submitting papers to specific law reviews.