The LA Times contains a searchable archive from 1990-present. Searching is free, but there is a charge for full text. Simple search and power search are available. This link leads to the search form for the New York Times Book section. To access this link, you must fill out a registration form.
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The New York Times contains an archive from 1980-present. The archive provides the full text of the reviews at no charge. Washington Post Provides the current issue of the Sunday section Book World. The Washington Post provides full-text of articles for the past two weeks free of charge. There is a separate searchable archive of articles dating from 1977 to the present, but there is a charge for full-text articles.