Shapiro charts the history of the varied attempts, starting in the late 18th century, to disprove William Shakespeare's authorship of his works. Essentially, these theories all boil down to the assumption that a middleclass character actor on the Elizabethan stage wouldn't have the education and acuity to produce Shakespeare's plays and verse, and also that the theater going public wouldn't have been able to understand them; in fact, that the works were coded, with either political, religious, psychological subtexts, or they were written for posterity. Or any mixture of the above.
For my part, I find all of the theories to break down under the application of Occam's Razor: whoever wrote the plays was a master of stagecraft, and who more likely than a character actor in a leading theater company, who probably spent his formative years with that company "doctoring" preexisting plays to fit the needs of the company?