There's been a lot of buzz about how Bergoglio is associated with the "conservative" lay ecclesial movement Communion and Liberation (CL)—similar to the Neo-Catechumenal Way, Foculare, and Opus Dei—founded by Luigi Giussani, whose funeral Ratzinger presided.

CL is thoroughly Modernist. It matters little that Bergoglio is a "social conservative"; if he's theologically heterodox, he's an enemy of the Faith, nothing short of being a Protestant.

De Lubac and Giussani are both New Theologians. They both believe in vital imminence, which is the destruction of the supernatural order (cf. Feingold's The Natural Desire to See God According to St. Thomas and His Interpreters and this The Thomist review of it).

As I wrote to a CL member recently:

 Thank you for your comments on my "The Religious Sense: Heretical or Not? You Decide." page. I was a part of CL for at least 3 years, so I know about Giussani, etc., but it wasn't until I read, re-read, and read again Pope St. Pius X's Lamentabili sane, Pascendi Dominici gregis (esp. these parts which struck me; cf. also Fr. Thwaites, SJ, reading it: part 1, part 2, part 3), and its drafter's (Fr. Lemius's) Catechism on Modernism that I really began to see that what the saintly pope so vehemently condemned appears nearly everywhere in the Church since Vatican II (neo-Modernism). Just as Pope Paul VI was prophetic in Humanæ Vitæ regarding the devastating consequences of contraception, so was Pope St. Pius X prophetic in Pascendi for seeing that in Modernism "the way is opened wide for atheism" (Pascendi §14).
 
  So, don't "be a man of one book" (or author). ☺ Read the saintly pope's encyclicals, other popes' encyclicals against modern errors, Fr. Lemius's Catechism on Modernism, and Fr. Dominique Bourmaud, O.P.'s 100 Years Of Modernism (in a library near you or for purchase), which gives you the philosophical basics to understand how modern philosophy opposes that of the Angelic Doctor, St. Thomas Aquinas, whose philosophy and theology so many popes magisterially recommend.
 
  "From beginning to end everything in it [Modernism] {i.e., agnostic, idealist philosophy, from which originates the Modernists' history and theology} is a priori, and a priori in a way that reeks of heresy." (Pascendi §33). This apriorism and "anthropolotry" (man-worship) is apparent in Giussani, e.g., where he says that "the criterion for judging this reflection on our own humanity must emerge from within the inherent structure of the human being" (The Religious Sense p. 15f.), not from external reality and Revelation "made credible by external signs" (Dei Filius). "There is no question now of the old error, by which a sort of right to the supernatural order was claimed for the human nature. "Than this there is surely nothing more destructive of the whole supernatural order." (Pascendi §10, where Pope St. Pius X first discusses "religious sentiment"/sense).

 Another very good, comprehensive "study of changes in the Catholic Church in the XXth century" is Romano Amerio's Iota Unum (in a library near you; first 15 chapters for free online).
 
  For a more theological perspective, see Fr. T. J. Walshe's adaptation and rearrangement of Fr. Garrigou-Lagrange, O.P.'s De Revelatione: The Principles of Catholic Apologetics: Study of Modernism based chiefly on the Lectures of Pere Garrigou-Lagrange, O.P.'s «De Revelatione per Ecclesiam Catholicam proposita» adapted and re-arranged.
 
  Aidan Nichols, O.P.'s excellent biography of Fr. Garrigou-Lagrange, Reason with Piety, begins with a very nice description/summary of Modernism; the rest of the work shows how Fr. Garrigou-Lagrange was the last great pre-Vatican II Thomist theologian and enemy of those for whom a "passion for novelty is always united "with hatred of scholasticism"* (Pascendi §42), viz., of the Modernist New Theologians (cf. his Where is the New Theology Leading Us? {he answers: back to Modernism}, The Structure of the Encyclical Humani Generis, and David L. Greenstock, T.O.P.'s "Thomism and the New Theology.").

    *Pope St. Pius X clarifies that by "scholasticism" he means the philosophy and theology of St. Thomas Aquinas: "let it be clearly understood above all things that the scholastic philosophy We prescribe is that which the Angelic Doctor has bequeathed to us." (Pascendi §45).

  Modernism essentially seeks to change truth from being the "adequation of intellect and thing" to being "the adequation of intellect and life." Modernism comes under another name: relativism, which Pope Benedict XVI certainly spoke out against during his pontificate.

(HTML to SMF code conversion courtesy this site, in case you were wondering ☺)

Fr. Garrigou-Lagrange, O.P.'s The Principles of Catholic Apologetics: A Study of Modernism Based Chiefly on the Lectures of Père Garrigou-Lagrange, O.P.'s «De Revelatione per Ecclesiam Catholicam proposita» Adapted and Re-Arranged contains a very good criticism of the "New Apologetic" (p. 28, 42-43) used by Giussani:

The method of Immanence…in human nature presupposes an exigency for the Supernatural
…
Before proceeding to note how the advocates of this new Apologetic regard criteria external and internal, the reader will distinguish [cf. Pascendi §19] between (i), the doctrine of "immanence," i.e. God's intimate presence in His creation of which the complementary truth is God's transcendence—acknowledged teaching of Catholic philosophy, and (ii), the doctrine of "immanence" in apologetics which accepts the internal religious sense as the only valid criterion of religious truth [cf. The Religious Sense p. 15]—one of the fundamental tenets of Modernism.
…
Criticism of the New Apologetic
1.— It is founded on Semi-Agnosticism, vis., the untrustworthiness of speculative reason. [Giussani: "The summit of the conquest of reason is the perception of an existing, unreachable unknown." (The Religous Sense p. 155-6)]
2.— It is founded also on an aspect of the doctrine of immanence. If Catholic Faith is demanded by our nature, that Faith is not in truth the supernatural. In truth the Supernatural is above not only the powers but the exigencies of human nature. These Apologists fail to see that it is natural happiness arising from the natural knowledge and love of God that our nature strives to attain. [cf. Feingold's The Natural Desire to See God According to St. Thomas and His Interpreters and this The Thomist review of it]
3. — The formal motive of Faith consists in the authority of God who reveals, and not in religious experience.

Bergoglio also wrote about Giussani's apologetics/theology, noting essentially what Lamentabili condemns in § "25. The assent of faith ultimately rests on a mass of probabilities."