Here is a sampling of what they had to say:
Rob Kendt in his Broadway.com Review: "Bennett's rip-roaringly enjoyable The History Boys is almost entirely a pedantic exercise; its point of view is never far from view. But Bennett possesses such a large and sympathetic vision, and such a smart ear for incisive, nearly Wildean language, that this teaching lesson is like none we ever received in school. Certainly director Nicholas Hytner's handsome, free-flowing, ideally cast production, which comes to us whole from London's National Theatre, helps Bennett's medicine go down smoothly. But the play's the thing, and in the midst of an intellectually challenged Broadway season, we might embrace The History Boys as a wise elder whose company enriches, even if the message he bears is a tad shopworn."
Clive Barnes of The New York Post: "Alan Bennett's The History Boys, which came to the Broadhurst Theatre last night trailing clouds of glory and awards from London's National Theatre, could well emerge as the cult hit of the season. So I'm sorry to say I found it hopelessly overblown, overhyped and overrated. Admittedly, it has one indelible stage portrait from Richard Griffiths—a hitherto underrated actor in the role of his lifetime—and beautifully calibrated performances from the terrific Frances de la Tour and an admirable newcomer, Stephen Campbell Moore. The play itself—despite what you'll hear elsewhere—isn't up to much, though it's full of sterling production values and deftly staged by Nicholas Hytner."
David Rooney of Variety: "This very British play from that peerless observer of English life, Alan Bennett, is in many ways sprawling and untidy, but invigoratingly alive with ideas. And Nicholas Hytner's superb production also is alive with an unruly energy that mirrors the sexual and intellectual vitality of the gifted lads at the play's center."
Michael Kuchwara of The Associated Press: "Directed by the National's artistic head, Nicholas Hytner, The History Boys is both intellectually rigorous and emotionally affecting. And very, very funny. It's filled with warm, often gentle humor, a comic spirit that grows out of situation and character."
Linda Winer of Newsday: "This is ebullient, crackling, miraculous theate—as moving as it is intellectually extravagant, as entertaining and humane as its description sounds Byzantine and overeducated. The impeccably smart and endearing young actors play together as if they've been embodying these characters for years."