"Blessed are the pure in heart, for they shall see God." The Catholic Church has always held that we shall "see" God. There is, however, controversy over what it means to "see God".
First, let it be said that from a Catholic point of view, God is incomprehensible. We are finite and He is infinite. We shall never fully comprehend or understand God. However, the Scriptures do affirm that we shall "see" God. Saint Thomas Aquinas drew a sharp line between "seeing the divine essence" and "comprehending the divine essence" (STh I, q. 12, a. 1, 7). The former (seeing) does not entail the latter (comprehending).
Thomas' distinction between seeing and comprehending has been contested, particularly by voices in the East inspired by Gregory Palamas. Palamas stated unequivocally that the blessed do not and will not see the divine essence, because God's incomprehensibility excludes "seeing" the divine essence. Instead, the Palamites propose the concept of "divine energies", which are described as a glorious light - the same light, they say, that was revealed at Christ's Transfiguration. For Palamites, seeing God must only refer to seeing the "divine energies" since the "divine essence" is closed off to us as incomprehensible.
It would not be honest to cite every Patristic quotation referring to "theosis" or "energeia" as evidence for the Palamite position. It is important to recognize that the Palamite position began first as a defense of Hesychism and then later became codified in the terminology of divine energies. Usage of "energeia" in the Fathers does not necessarily mean that the Fathers employed the term with the fully loaded distinctions that some Palamites infer.
I will grant that there are some pretty hairy passages in the Fathers with respect to divine incomprehensibility and "seeing". Thomas Aquinas is aware of them. Here are two "problem passages" that Thomas identifies.
For Chrysostom (Hom. xiv. in Joan.) commenting on John 1:18, "No man hath seen God at any time," says: "Not prophets only, but neither angels nor archangels have seen God. For how can a creature see what is increatable?"This turns out to be a rhetorical question since Saint John Chrysostom goes on to say that he is speaking of a mode of comprehension as regards the way in which the Persons of the Trinity know and see one another. Obviously, created agents do not comprehend or see in this way because we are created and finite, whereas the Divine Persons are not.
A second problem passage:
Dionysius also says (Div. Nom. i), speaking of God: "Neither is there sense, nor image, nor opinion, nor reason, nor knowledge of Him."Thomas appeals to the context of this statement in Divine Names. Prior to the statement of above, the Areopagite says: "He is universally to all incomprehensible," so that this statement does not refer to the blessed in particular. As Thomas states, this is a reference to the "vision of comprehension" which is in fact impossible.
Critics of Aquinas assume that he believes that the human intellect is capable of comprehending the divine essence. This is clearly false given the passages above. Instead, Thomas states that the blessed angels and humans are made "deiform" so that they can see the divine essence (see Summa theologia I, q. 12, a. 5). Thomas also repeatedly refers to this as the created "light of glory" which is the means by which the blessed are elevated to this beatific vision.
Some have said that Aquinas and Palamas may be reconciled, but I don't see how we can reconcile Thomas' conviction that "we see the divine essence with Palamas' conviction that we don't see the divine essence, only the energies. Certainly, both believe that we "see God". In this sense they can be reconciled. However, Palamas' denial of the magisterial teaching that the blessed shall "see the divine essence" is contrary to the Catholic Faith.
The real kicker is that an Ecumenical Council has made a declaration on the matter. The Council of Vienne in 1311-2 decreed that the blessed to "see the divine essence". Thus, the Palamite position is not strictly acceptable for the magisterial Catholic since Palamas assumes the opposite.
The Council of Vienne condemned eight propositions - one of which highlights the magisterial weight of the idea that we see God by the light of glory: "Fifthly, that any intellectual nature in itself is naturally blessed, and that the soul does not need the light of glory to elevate it to see God and enjoy him blissfully."
The best magisterial source, though, is the constitution issued by Pope Benedict XII in 1336 Benedictus Deus, which sets the record straight once and for all:
Since the passion and death of the Lord Jesus Christ, these souls have seen and see the divine essence with an intuitive vision and even face to face, without the mediation of any creature by way of object of vision; rather the divine essence immediately manifests itself to them, plainly, clearly and openly, and in this vision they enjoy the divine essence . Moreover, by this vision and enjoyment the souls of those who have already died are truly blessed and have eternal life and rest. Also the souls of those who will die in the future will see the same divine essence and will enjoy it before the general judgment.If you follow Palamas, this paragraph is difficult because it states that we see the "divine essence" - a proposition denied by Gregory Palamas.
[Again, I'm not contesting the sanctity of Gregory Palamas. He was a holy man. Thomas Aquinas is a saint and a doctor of the Church and yet he was wrong about the Immaculate Conception and the proper matter of Holy Orders. I'm only saying that Palamas' denial of the vision of God's essence is contrary to Papal and Conciliar decrees.]