While these theatre-related databases don't just search newspapers for reviews, they do include them. (Newspapers are another good source for reviews.)
These print resources are mostly collections of newspaper reviews, which can be searched by play, playwright, or performers. If you'd like to search by a specific playwright, however, you can also try looking in the various bio-bibliographies in the MPAL reference section under the Z8196's.
One of the best ways to find works of criticism on theatre topics is running a subject search. Subjects are assigned to items in strings that follow certain rules. For this topic, your string should start with:
If you search for "Drama" as a subject, it will return all related items. You can narrow these results by adding a time period:
Drama -- 19th century or Drama -- 20th century
You can narrow this further and specifically target works of criticism:
Drama -- 19th century -- History and Criticism
If you're still getting too many results or have something very specific in mind, you can narrow even further:
Drama -- 19th century -- History and Criticism -- Bibliography
Drama -- 19th century -- History and Criticism -- Periodicals
If you search for "Theater" you can add the phrase "History and Criticism" without a region or time period:
Theater -- History and Criticism
You can also add information about a country or region
African drama - History and criticism
Theater - Nigeria (In English) - 20th Century
If you find that you're having difficulty using the catalog or finding the kind of information you're looking for, please don't hesitate to ask for help!